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ุฅุฐุง ุงู„ุดุฑูƒุฉ ุชุฑุบุจ ููŠ ุงุฎุชุจุงุฑ ู‡ุฐู‡ ุงู„ูุฑุถูŠุฉ ูˆููŠู‡ุง
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ุงุนุชุจุงุฑ ุฃู† ุงู„ู…ุดุงุฑูƒุฉ ู…ุณุชุนู…ู„ุฉ ุจุดูƒู„ ุนุงู… ูุจุงู„ุชุงู„ูŠ
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ู†ุณุชุทูŠุน ุงุณุชุฎุฏุงู… ุชุฌุงุฑุฉ ุงู„ู€ T ู„ุฃู† ุงู„ูุฑุถูŠุฉ ู‡ูŠ ุฃู‚ู„ ู…ู†
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52 ุจูŠุฑู…ุงู† ู‡ุฐุง ู…ุง ู†ุฑูŠุฏู‡ ุฃู† ู†ูุนู„ ุทุจุนุงู‹ ุงู„ูุฑุถูŠุฉ
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ู…ูƒุชูˆุจุฉ 152 ุฃูˆ ุฃู‚ู„ ู…ู† 152
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ุงู„ุขู† ุจุญูƒูŠ suppose alpha is 10% ูŠุนู†ูŠ ุงู„ู€ alpha is given
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to be 10% ูˆ ุงู„ู€ sample size 25 ูŠุนู†ูŠ ุฃุชุงู†ูŠ ุงู„ู€ sample
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size 25 ุจู†ุฏู‚ู†ุง ู†ุญู„ ุงู„ุณุคุงู„ ูˆู†ุทู„ุน ุงู„ู€ rejection
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region ู‡ุฐุง ุจุญูƒูŠ ุนู„ู‰ one tailed test ุชุจุชุฏุฆ
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ุงู„ูƒู„ุงู… ุนู„ู‰ ุงู„ู€ upper tail ูู‡ุฐู‡ ุงู„ู†ู‚ุทุฉ ุงู„ู„ูŠ ู‡ู†ุง ู„ุงุฒู…
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ุฃุทู„ุนู‡ุง ู…ู† ุฃูŠู†ุŸ ู…ู† ุงู„ู€ table ูู‡ุฐู‡ ุงู„ู€ critical value
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ุฃุณู…ูŠู‡ุง T D F ูˆ ุงู„ู€ Alpha ู‡ูŠูƒ ุชูƒุชุจ ุทุจุนุงู‹
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degrees of freedom N equals 25 ุจุงู„ุชุงู„ูŠ ุงู„ู€ minus
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one it gives 24 24 ูˆ 10% ูุจูุชุญ ุฌุฏูˆู„ ุงู„ู€ T-test ุจู†ุนู…ู„
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ู„ู€ 24 degrees of freedom
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ู„ุฃู†ู‡ุง 24 ูˆ under 10%
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ูุงู„ู€ critical value 1.318 ุซู… ู†ู‚ูˆู„ ุฅุฐุง ูƒุงู†ุช ุงู„ู€ test statistic ุชุณู‚ุท ููŠ ุงู„ู…ู†ุทู‚ุฉ ุงู„ุญุฑุฌุฉ
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ุงู„ุชูŠ ุฃูƒุจุฑ ู…ู† 1.
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318 ูู†ู‚ูˆู„ ุฅุฐุง
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ูƒุงู†ุช ุงู„ู€ test statistic ุฃูƒุจุฑ ู…ู† 1.318 ู„ู…ุงุฐุง ุฃูƒุจุฑ ู…ู†ุŸ ู„ุฃู†ู†ุง
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ู†ุฌุฑุจ ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
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ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฅุฐุง ูƒุงู†ุช ุงู„ู€ test statistic ุฃูƒุจุฑ ู…ู† 1.318.
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ุงู„ุขู† ูŠุฌุจ ุฃู† ู†ู‚ูˆู… ุจู…ู‚ุงุฑู†ุฉ ู‚ูŠู…ุฉ ุงู„ูุฑุถูŠุฉ.
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ู„ุฐู„ูƒ ููŠ ู‡ุฐู‡ ุงู„ุญุงู„ุฉ ูŠุฌุจ ุฃู† ู†ุญุตู„ ุนู„ู‰ ู…ุฌู…ูˆุนุฉ ูˆู†ู‚ูˆู…
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ุจู…ู‚ุงุฑู†ุฉ ู‚ูŠู…ุฉ X ูˆู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู…ู‚ุงุฑู†ุฉ
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X.ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X
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.ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X
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.ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X
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.ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ู‚ูŠู…ุฉ X. ุฅุฐุง ู‡ุฐู‡
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ุงู„ู€ X bar ูˆ ุงู„ู€ S are given both for the sample
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Now it's easy to compute the test statistic by
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using the formula we know X bar minus mu
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over S over root N So X bar minus the mean S over
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square root of N Now straightforward calculations
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you can get the result of X bar 53 ุงู„ุขู† ฮผ
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ุฃูƒุซุฑ ู…ู† 52 ฯƒ ู‡ูˆ 10 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n
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ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25 n ุนู…ุฑู‡ 25
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ุงู„ุขู† ูŠุฌุจ ุฃู† ุชู‚ุงุฑู† ู‚ูŠู…ุฉ ุงู„ู€ T ู…ุน ุงู„ู…ู†ุทู‚ุฉ
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ุงู„ุญุฑุฌุฉ ุงู„ุขู† ุงู„ุณุคุงู„ ู‡ูˆ ู‡ู„ ู‡ุฐู‡ ุงู„ู‚ูŠู…ุฉ ู…ูˆุฌูˆุฏุฉ ููŠ
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ุงู„ู…ู†ุทู‚ุฉ ุงู„ุญุฑุฌุฉุŸ
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ูˆุงุถุญ ุฃู† ุงู„ู€ 0.55 ู…ูˆุฌูˆุฏุฉ ููŠ ุงู„ู…ู†ุทู‚ุฉ ุงู„ุญุฑุฌุฉ ุจุงู„ู†ุณุจุฉ
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ู„ู‡ุฐุง ุงู„ุณุจุจุŒ ู„ุง ู†ู‚ุจู„ ุงู„ูุฑุถูŠุฉ ุงู„ุตูุฑูŠุฉ ุฅุฐุง ู„ู… ุฃุฑูุถู‡ุง
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ู‡ุฐุง ู…ุนู†ุงู‡ ู…ุงุฐุงุŸ ุงู„ู€ Managerial ConclusionุŒ ู„ุง ูŠูˆุฌุฏ
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ุฏู„ูŠู„ ูƒุงููŠ ู„ุฅุธู‡ุงุฑ ุฃู† ู…ู‚ุงู„ ุงู„ู€ True Mean ู‡ูˆ ุฃูƒุซุฑ
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ู…ู† 52
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ููŠ ุณุคุงู„ ูˆุงุถุญ ู†ูุณ ุงู„ููƒุฑุฉ ุงู„ู„ูŠ ุญูƒูŠู†ุงู‡ุง ุงู…ุจุงุฑุญ ู„ูƒู†
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ุงู„ุงุฎุชู„ุงู ุจุณ ุจุฏู„ ู…ุง ูƒุงู†ุช two-tailed ุงู„ุขู† ูƒุงู†ุช one
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-tailed the other side on the other hand we can
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compute the p-value because we mentioned yesterday
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there are two ways or two approaches for
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conducting the test one is called a critical value
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approach this is a critical value and the other
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one is called p-value approach ุจุงู„ูุฑุถ T-table ุชุนุทูŠ
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ู†ุชูŠุฌุฉ ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ู„ุชุฌุงุฑุจ ุจู‚ูŠู… ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจู‚ูŠู…
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ุชู‚ุฑูŠุจูŠุฉ ู„ู„ุชุฌุงุฑุจ ุจ
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Probability of T greater than ... ุงู„ุนู†ูˆุงู† ู‡ู†ุง ู‡ูˆ
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ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
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ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
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ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
78
00:06:39,640 --> 00:06:40,860
ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
79
00:06:40,860 --> 00:06:41,700
ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
80
00:06:41,700 --> 00:06:44,640
ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ
81
00:06:44,640 --> 00:06:49,220
ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠุณ ู‚ูŠู… ุชุฌุงุฑุจ ุงู„ุชุฌุงุฑุจ ู„ูŠ
82
00:06:50,380 --> 00:06:56,180
ูุจุฃุฎุฐ ุนู†ุฏ ุงู„ู€ 0.55 ู‡ุฐู‡ ู…ู‡ู…ุฉ ุฌุฏุงู‹ ูŠุนู†ูŠ ุฃูƒุจุฑ ู…ู†
83
00:06:56,180 --> 00:06:58,520
ุงู„ู€ 0.55 ู…ุด ุฃูƒุจุฑ ู…ู† ุงู„ู€ 1.31
84
00:06:58,520 --> 00:07:01,860
8 ู…ุด ุนู„ุงู‚ุฉ ุจู‡ุฐู‡ ูŠุนู†ูŠ ุจุดูˆู ุงูŠุด ุงุญุชู…ุงู„ ุชูƒูˆู† ุงู„ู€
85
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test statistic ุฃูƒุจุฑ ู…ู† ุงู„ู€ test value ุงู„ู„ูŠ ู‡ูˆ 0.
86
00:07:04,640 --> 00:07:09,500
55 now in this case just backward
87
00:07:09,500 --> 00:07:13,500
calculation this is my t table again we have to
88
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look at degrees of freedom 24 and search
89
00:07:19,520 --> 00:07:24,540
for the value of 0.55 ุฃุฏูˆุฑ ุนู„ู‰ ุงู„ู‚ูŠู…ุฉ 0.55 ู…ู†
90
00:07:24,540 --> 00:07:28,900
ู‡ู†ุง for sure the table will not give all values so
91
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we are looking for the closest value of 0.55
92
00:07:34,440 --> 00:07:38,860
ูŠุนู†ูŠ ุจุฏูˆุฑ ุนู„ุดุงู† ุฃู‚ุฑุจ ู‚ูŠู…ุฉ ุจู…ุดูŠ ุนู„ู‰ ุงู„ู€ 24 ููŠ ุนู†ุฏ 0.
93
00:07:38,860 --> 00:07:46,570
685 ุจุนุฏูŠู† ุจุฒูŠุฏ ู…ุธุจูˆุท ู…ุน ูƒุฏู‡ ุฃู‚ุฑุจ ู‚ูŠู…ุฉ ู…ู† ู‡ุชูƒูˆู† ู‡ูŠ
94
00:07:46,570 --> 00:07:49,670
ู‡ุฐู‡ ูˆุงุถุญุฉ ุฅุฐุง ู…ุง ููŠุด ุนู†ุฏูŠ ุญุงุฌุฉ ุงุณู…ู‡ุง 0.5
95
00:07:49,670 --> 00:07:54,170
5 ุจุฃุฎุฐ ู…ุงุฐุงุŸ ุฃู‚ุฑุจ ู‚ูŠู…ุฉ ู„ู‡ุง 0.685
96
00:07:54,170 --> 00:07:58,010
ุฅุฐุง ู…ุงู„ูƒ ุฏู‡ ุงู„ุฌูˆุงุจ ู‡ุชุทู„ุน ู…ุนุงู‡ ุชู‚ุฑูŠุจุงู‹ ู…ุด exact
97
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result ุงูŠุด ุจุชุณุงูˆูŠุŸ 0.25 ู…ู† ู‡ุฐู‡ุŒ ุฅุฐุง 0.2
98
00:08:05,490 --> 00:08:12,190
5 ุทุจ ู…ู† ูˆุฌู‡ุฉ ู†ุธุฑูƒ ู‡ูŠ ุฃูƒุจุฑ ู…ู† 0.25
99
00:08:12,190 --> 00:08:21,360
ูˆู„ุง ุฃู‚ู„ุŸ ู„ุญุธุฉ ูˆุฃู†ุง ู…ุงุดูŠ ู‡ูŠูƒ ุงู„ู€ P-value ู…ุงู„ู‡ุง ู‡ูŠูƒ
100
00:08:21,360 --> 00:08:25,040
ู‡ูŠูƒ ุชูƒุจุฑ ... ุชูƒุจุฑ ... 0.25, 0.20, 0.15,
101
00:08:25,040 --> 00:08:28,900
0.10, ุจุชุตุบุฑ ุทูŠุจ ุฃู†ุง ุฃู‚ูŠู… ุงู„ู„ูŠ ุฃู†ุง ุนุงูŠุฒู‡ุงุŒ ู…ุงุดูŠ ุนู„ู‰
102
00:08:28,900 --> 00:08:32,900
ุงู„ูŠู…ูŠู† ูˆู„ุง ุฌุงูŠ ุนู„ู‰ ุงู„ุดู…ุงู„ุŸ ุฌุงูŠ ู‡ูŠูƒ ุงู„ู€ 0.55
103
00:08:32,900 --> 00:08:40,660
ู‡ู†ุงุŒ ู…ุธุจูˆุทุŸ ู…ุน ูƒุฏู‡ ุงู„ู€ P-value ุชุจุนุช ู‡ู†ุง ูŠุนู†ูŠ ุงู„ู€
104
00:08:40,660 --> 00:08:43,660
result ุตุญ ุญูˆุงู„ูŠ ุงู„ู€ 0.25, ุจู‚ูˆู„ูƒ ุฅู†ู‡ุง ู…ุงู„ู‡ุง
105
00:08:45,230 --> 00:08:51,630
ุฃูƒูŠุฏ ุฃูƒุจุฑ ู…ู† 25% either way if you just mention
106
00:08:51,630 --> 00:08:55,630
it's approximately 0.25 or greater than 0.25 you
107
00:08:55,630 --> 00:08:58,850
have to compare this P-value with ฮฑ now ฮฑ
108
00:08:58,850 --> 00:09:03,390
is given to be 10% is your P-value greater than
109
00:09:03,390 --> 00:09:11,390
ฮฑ in other words is 0.25 ููŠ ู…ู‡ุฏูŠ ุฃูƒุจุฑ ู…ู† 0.10
110
00:09:14,120 --> 00:09:21,480
ุจุงู„ู„ู‡ ุนู† ุฌุฏ 25% ุฃูƒุจุฑ ูˆู„ุง ุฃุตุบุฑ ู…ู† 0.10 ู‡ุฏ
111
00:09:21,480 --> 00:09:26,180
ุฃูƒุจุฑ ูˆู„ุง ุฃุตุบุฑุŸ ู‡ุฏ ูƒุฏู‡ ู…ุฑุชูŠู† ูˆู†ุตู ุชู‚ุฑูŠุจุงู‹ ุฃูƒุจุฑ ู…ุธุจูˆุท
112
00:09:26,180 --> 00:09:29,380
ุทุจ ู„ู…ุง ุชูƒูˆู† ุฃูƒุจุฑ we reject ูˆู„ุง don't rejectุŸ don't
113
00:09:29,380 --> 00:09:34,740
reject ู…ุน ูƒุฏู‡ ู…ุง ุทู„ุนุชุด ุจู†ูุณ ุงู„ู€ conclusion ุงู„ุฃูˆู„ ุฅุฐุง
114
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ุงู„ู€ both cases we don't reject on the hypothesis ุฅุฐุง
115
00:09:38,590 --> 00:09:43,370
ุงู„ู€ 0.25 ู‡ูˆ ุฃูƒุซุฑ ู…ู† 10% ู„ุฐู„ูƒ ู„ุง ู†ู‚ุจู„ ุฃูŠุถุงู‹ ุงู„ู€ null
116
00:09:43,370 --> 00:09:48,850
hypothesis ู‡ุฐุง ูŠุนู†ูŠ ุฃู†ู‡ ู„ุง ูŠูˆุฌุฏ ุฏู„ูŠู„ ูƒุงููŠ ู„ุฅุฏุงุฑุฉ
117
00:09:48,850 --> 00:09:52,630
ุงู„ู€ alternative hypothesis ุงู„ุชูŠ ุชุดูŠุฑ ุฅู„ู‰ ุฃู† ุงู„ุนู…ูŠู„
118
00:09:52,630 --> 00:10:00,670
ุงู„ู…ุณุชู‚ุจู„ูŠ ุฃูƒุซุฑ ู…ู† ุฃูˆ ุฃูƒุซุฑ ู…ู† 52$ ุทุจุนุงู‹
119
00:10:00,670 --> 00:10:05,310
ุงู„ุฅุฌุงุจุฉ ุงู„ุตุญูŠุญุฉ ุงู„ุชูŠ ุฃุนุทุงู†ูŠ ุฅูŠุงู‡ุง ุงู„ูƒุชุงุจ ู‡ู†ุง ู‡ูˆ 0.2937 ู‡ุฐุง
120
00:10:05,310 --> 00:10:10,320
ู‡ูˆ ุงู„ู†ุชูŠุฌุฉ ุงู„ุตุญูŠุญุฉ ุทุจุนุงู‹ ุงุญู†ุง ุทู„ุนู†ุง 0.25 ูˆุญูƒูŠู†ุง
121
00:10:10,320 --> 00:10:14,160
ุฃูƒุจุฑ ู…ู† ุงู„ู€ 0.25 ูุญู„ูŠู†ุง ุชู‚ุฑูŠุจุงู‹ ุญุงู„ู†ุง ู…ุงุดูŠุฉ ุนู„ู‰ ู†ูุณ
122
00:10:14,160 --> 00:10:21,300
ุงู„ูˆุซูŠู‚ุฉ ู‡ุฐุง ูƒุงู† ุจุงู„ู†ุณุจุฉ ู„ู„ุฌุฒุก ุงู„ู„ูŠ ุชุจู‚ู‰ ุงู…ุจุงุฑุญ ููŠ
123
00:10:21,300 --> 00:10:27,300
ุฃูŠ ุณุคุงู„ุŸ ุทุจ ู…ูˆุถูˆุน ุงู„ูŠูˆู…ุŒ ู…ูˆุถูˆุน ุงู„ูŠูˆู… ู‡ูŠุญูƒูŠ ุนู„ู‰
124
00:10:27,300 --> 00:10:31,580
ู…ูˆุถูˆุน ู…ู‡ู… ุงู„ู„ูŠ ู‡ูˆ hypothesis test for proportions
125
00:10:34,990 --> 00:10:39,710
ุฎู„ุงุต ู‡ุจุฏุฃ ู…ูˆุถูˆุน ุฌุฏูŠุฏ I put this test for in
126
00:10:39,710 --> 00:10:43,410
proportions ู‡ุนุทูŠูƒูŠ ููƒุฑุฉ ุนู„ู‰ ุงู„ู…ูˆุถูˆุน ุงู„ู„ูŠ ูุงุช
127
00:10:43,410 --> 00:10:47,830
ูˆู…ูˆุถูˆุน ุงู„ูŠูˆู… ุงู„ููƒุฑุฉ ุงู„ู„ูŠ ุฃุฎุฏู†ุงู‡ุง ูƒุงู†ุช ู†ุณุชุฎุฏู… ูƒู„ุงู…
128
00:10:47,830 --> 00:10:53,630
ุนู„ู‰ numerical values ุฒูŠ phone bills ุฒูŠ ุงู„ู€ wages ุฒูŠ
129
00:10:53,630 --> 00:10:59,970
ุงู„ู€ ages ุฒูŠ ุงู„ู€ weights and so on so we focus on
130
00:10:59,970 --> 00:11:03,260
population means ู„ุฐุง ุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ู€ population mean
131
00:11:03,260 --> 00:11:07,680
ูˆูƒู†ุง ุจู†ุญูƒูŠ ุนู„ูŠู‡ ุนู„ู‰ data numeric ู…ุชุบูŠุฑุงุช ุฑู‚ู…ูŠุฉ
132
00:11:07,680 --> 00:11:13,560
ุงู„ู†ูˆุน ุงู„ุซุงู†ูŠ ู…ู† ุงู„ู€ data ุงู„ู„ูŠ ู‡ูŠ ุจู†ุช ู…ุด ุฑู‚ู…ูŠุฉ ู…ุณู…ู‰
133
00:11:13,560 --> 00:11:17,020
qualitative data ูุงู„ู€ qualitative ู…ุง ูŠู†ูุนุด ู†ุณุชุฎุฏู… ุงู„ู€
134
00:11:17,020 --> 00:11:21,180
mean ุฒูŠ ู…ุง ุฃุฎุฏู†ุง ููŠ chapter 7 ุฃุฎุฏู†ุง sampling
135
00:11:21,180 --> 00:11:24,620
distribution ู„ู„ู€ mean ูˆ sampling distribution ู„ู„ู€
136
00:11:24,620 --> 00:11:29,900
mean ุฃุฎุฏู†ุง ุดุบู„ุชูŠู† sampling ู„ู„ู€ mean ูˆ ุงู„ู€ mean
137
00:11:29,900 --> 00:11:30,340
ุงู„ุซุงู†ูŠุฉ
138
00:11:35,000 --> 00:11:37,400
ุฃุฎุฐู†ุง ุงู„ู€ Sampling Distribution of the Sample Mean
139
00:11:37,400 --> 00:11:41,500
ูˆ ู„ู„ู€ Proportion ุจุฑุถู‡ ู„ุฃู† ู†ูุณ ุงู„ุฌุฒุก ุณู†ุงุฎุฏ ุงู„ู€
140
00:11:41,500 --> 00:11:46,280
Hypothesis Test for Proportions ุฅุฐุง ู‡ุฐุง ุงู„ุฌุฒุก
141
00:11:46,280 --> 00:11:48,860
ุงู„ุซุงู†ูŠ ู„ู†ุฎุชู…ู‡ ุจู€ Chapter 9
142
00:12:19,140 --> 00:12:21,620
ุจุณ ู‡ุชุดูˆู ุงู„ู†ุชูŠุฌุฉ ู…ู† ุนู†ุฏ ุงุจุญุซ ุนู†ู‡ุง
143
00:12:47,410 --> 00:12:55,310
ุณู†ู‚ูˆู… ุจุงุฎุชุจุงุฑ ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช
144
00:12:55,310 --> 00:13:01,630
ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช
145
00:13:01,630 --> 00:13:04,830
ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช
146
00:13:04,830 --> 00:13:05,430
ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช
147
00:13:05,430 --> 00:13:06,300
ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช ุงู„ูุฑุถูŠุงุช ู„ุงุฎุชุจุงุฑุงุช
148
00:13:06,300 --> 00:13:11,080
ู„ู„ุณู…ุงุช ุงู„ู…ุฌุชู…ุนูŠุฉ ูˆุงู„ุขุฎุฑ ู„ุณู…ุงุช ุงู„ู…ุฌุชู…ุนูŠุฉ
149
00:13:11,080 --> 00:13:17,680
ุจุงู„ู…ู‚ุงุฑู†ุฉ ูŠุฌุจ ุฃู† ุชู‚ุฑุฑ ุจูŠู† ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ูˆุงุฎุชุจุงุฑุงุช
150
00:13:17,680 --> 00:13:18,200
ุงู„ุงุฎุชุจุงุฑุงุช ูˆุงู„ุงุฎุชุจุงุฑุงุช ูˆุงู„ุงุฎุชุจุงุฑุงุช ูˆุงู„ุงุฎุชุจุงุฑุงุช
151
00:13:18,200 --> 00:13:18,440
ูˆุงู„ุงุฎุชุจุงุฑุงุช ูˆุงู„ุงุฎุชุจุงุฑุงุช ูˆุงู„ุงุฎุชุจุงุฑุงุช
152
00:13:18,440 --> 00:13:33,500
ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช ุงู„ุงุฎุชุจุงุฑุงุช
153
00:13:34,820 --> 00:13:37,520
ู„ู„ุนูŠู†ุงุช ู„ู„ู€ statistics ุฒูŠ ุงู„ู€ sample mean ุฃูˆ ุงู„ู€
154
00:13:37,520 --> 00:13:41,340
sample proportion ู„ูƒู† ู„ู…ุง ู†ุชูƒู„ู… ุนู† ุงู„ู€ testing ุฃูˆ
155
00:13:41,340 --> 00:13:44,820
hypothesis testing ุจุชูƒูˆู† is about ุงู„ู€ population
156
00:13:44,820 --> 00:13:47,980
parameter ูˆุงุถุญุŸ ูุงู„ูุฑู‚ ุจูŠู† ุงู„ุงุซู†ูŠู† ุงู„ู€ sampling
157
00:13:47,980 --> 00:13:51,320
distribution ุจุชุชูƒู„ู… ุนู„ู‰ ุงู„ู€ sample statistic ู‡ู†ุง
158
00:13:51,320 --> 00:13:54,160
ุจุชุชูƒู„ู… ุนู† ุงู„ู€ population parameters ู‡ุฐู‡ ุงู„ูุฑู‚ ุจูŠู†
159
00:13:54,160 --> 00:13:59,630
ุงู„ุงุซู†ูŠู† ุงู„ู€ ... ุงู„ู€ proportion ู…ุน ูƒุฏู‡ these problems
160
00:13:59,630 --> 00:14:03,210
involve categorical variables ูŠูƒูˆู† ุนู†ุฏูŠ ุงู„ู…ุชุบูŠุฑุงุช
161
00:14:03,210 --> 00:14:07,550
ุบูŠุฑ ูƒู…ูŠุฉ ู†ูˆุนูŠุฉ in this case there are two possible
162
00:14:07,550 --> 00:14:12,870
outcomes ููŠ ุนู†ุฏูŠ ู†ุชูŠุฌุชูŠู† possess characteristic
163
00:14:12,870 --> 00:14:17,170
of interest or does not possess characteristic of
164
00:14:17,170 --> 00:14:22,720
interest for example suppose ุฃุณุฃู„ ุณุคุงู„ ู‡ู„ ุชูุถู„ ู‡ุฐุง
165
00:14:22,720 --> 00:14:28,420
ุงู„ู†ูˆุน ู…ู† ุงู„ู‚ู‡ูˆุฉุŸ ูุงู„ุฌูˆุงุจ ูŠู…ูƒู† ุฃู† ูŠูƒูˆู† ุฅู…ุง ู†ุนู… ุฃูˆ
166
00:14:28,420 --> 00:14:36,820
ู„ุงุŒ ูู‡ู†ุงูƒ ุงุชูุงู‚ูŠู† ุฅู…ุง ู†ุนู… ุฃูˆ ู„ุง. ู†ุฌุงุญ ุฃูˆ ุฎุณุงุฑุฉุŸ
167
00:14:36,820 --> 00:14:40,840
ุงุชูู‚ ุฃูˆ ู„ุง ุฃุชููู‚ุŸ ู‡ุฐุง ุงู„ู†ูˆุน ู…ู† ุงู„ุณุคุงู„ูŠู† ูŠุนู†ูŠ ุฃู†
168
00:14:40,840 --> 00:14:46,260
ู‡ู†ุงูƒ ุงุชูุงู‚ูŠู† ุฃูˆ ู„ุง ุฃุชููู‚ุŸ ู†ุชูŠุฌุชูŠู† ูˆุงุญุฏุฉ ุฃู†ุง ู…ู‡ุชู…
169
00:14:46,260 --> 00:14:47,960
ุจู‡ุง ุงู„ู†ุฌุงุญ
170
00:14:50,190 --> 00:14:56,950
Success or fail the exam fraction or proportion of
171
00:14:56,950 --> 00:14:59,490
the population in the category of interest is
172
00:14:59,490 --> 00:15:08,230
denoted by ฯ€ ู†ุฃุฎุฐ ฯ€ ุงู„ู€ population proportion
173
00:15:08,230 --> 00:15:11,490
ุฒูŠ ู…ุง ุฃุฎุฐู†ุง ููŠ Chapter 7 ฯ€ ูƒุงู†ุช population
174
00:15:11,490 --> 00:15:15,110
proportion ุจุฑุถู‡ ู†ุฃุฎุฐ ฯ€ ุนุจุงุฑุฉ ุนู† population
175
00:15:15,110 --> 00:15:20,800
proportion and in general this ฯ€ ู…ู‚ุงุฑู†ุฉ ุจูŠู† 0 ูˆ1
176
00:15:20,800 --> 00:15:24,440
ู…ู‚ุงุฑู†ุฉ ุจูŠู† 0 ูˆ1 ู…ู‚ุงุฑู†ุฉ ุจูŠู† 0 ูˆ1 ู…ู‚ุงุฑู†ุฉ ุจูŠู† 0 ูˆ1
177
00:15:24,440 --> 00:15:27,700
ู…ู‚ุงุฑู†ุฉ
178
00:15:27,700 --> 00:15:30,600
ุจูŠู† 0 ูˆ1 ู…ู‚ุงุฑู†ุฉ ุจูŠู† 0 ูˆ
216
00:18:14,510 --> 00:18:17,970
ุชุฑูƒุจูŠู‡ู… ู…ุด ุนู„ู‰ ุจุนุถ ุทู„ุน ุงู„ mean ู„ู„ ุจูŠ ุงู„ู„ูŠ ู‡ูŠ ุงู„
217
00:18:17,970 --> 00:18:21,790
ุจุงูŠ ู„ุญุงู„ู‡ุง ูˆุทู„ุน ุงู„ sigma ู„ู„ ุจูŠ ุงู„ู„ูŠ ู‡ูŠ ุงู„ู‚ูŠู…ุฉ ู‡ุฐู‡
218
00:18:21,790 --> 00:18:27,470
ูˆุจุนุฏูŠู† ุฏุฎู„ูŠู‡ู… ููŠ ุจุนุถ ู‡ูŠูƒ ุงู„ุณู„ุงู„ุฉ ุฅุฐุง ู‡ุฐูŠ
219
00:18:27,470 --> 00:18:30,690
statistic ุจูŠ minus ุจุงูŠ over ุจุงูŠ one minus ุจุงูŠ over
220
00:18:30,690 --> 00:18:35,030
n ุงู„ test
221
00:18:37,630 --> 00:18:44,350
ู‡ูŠ 0 ุถุฏ ูƒู„ ูˆุงุญุฏ ู„ูƒูŠ ู†ุญุตู„ ุนู„ู‰ ู†ุชูŠุฌุฉ ุฌูŠุฏุฉ ุฃูˆ ู†ุชูŠุฌุฉ
222
00:18:44,350 --> 00:18:48,530
ุตุญูŠุญุฉ ูŠุฌุจ ุฃู† ูŠูƒูˆู†ูˆุง ุงู„ุงุซู†ูŠู† ุงู„ูˆุงุถุญูŠู† ู…ูู‡ูˆู…ูŠู† ู† ููŠ
223
00:18:48,530 --> 00:18:53,530
ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„
224
00:18:53,530 --> 00:19:00,270
ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5
225
00:19:00,270 --> 00:19:00,390
ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ
226
00:19:00,390 --> 00:19:00,830
ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„
227
00:19:00,830 --> 00:19:01,270
ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5
228
00:19:01,270 --> 00:19:03,550
ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ
229
00:19:03,550 --> 00:19:04,390
ุฃู‚ู„ ู…ู† 5 ูˆู† ููŠ
230
00:19:07,810 --> 00:19:11,810
this case is not discussed in this chapter ูŠุนู†ูŠ ู„ูˆ
231
00:19:11,810 --> 00:19:15,870
ูƒุงู† ุงู„ุดุฑุท ูŠุนู†ูŠ ู…ุด ู…ุชุญู‚ู‚ูŠู† ุญุชู‰ ูˆุงุญุฏ ู…ู†ู‡ู… ู…ุด ู‡ูƒู…ู„
232
00:19:15,870 --> 00:19:21,230
ู„ุฃู† ุงู„ุฌุฒุก ู‡ุฐุง ู…ุด ู…ุดุฑูˆุน ููŠ ุงู„ class ุทุจุนุง ุฅุฐุง ุนุดุงู†
233
00:19:21,230 --> 00:19:23,690
ุฃุณุงุณ ุฃู‚ุฏุฑ ู†ุนู…ู„ ุงู„ proceeding ู„ู„ู…ุซู„ุฉ ู„ุงุฒู… ูŠูƒูˆู†
234
00:19:23,690 --> 00:19:28,110
under two conditions ู‡ุฏูˆู„ ู…ุง ู„ู‡ู… satisfied
235
00:19:33,570 --> 00:19:38,790
ุงู„ู€ Z statistic ู…ู…ูƒู† ุงูƒุชุจู‡ ุจุดูƒู„ ุจุฏู„ ู…ูƒุชุจ B ู…ู…ูƒู†
236
00:19:38,790 --> 00:19:45,290
ุงูƒุชุจ X ุจุฏู„ู‡ุง ู…ุทู„ุน ุงู„ X ุนุจุงุฑุฉ ุนู† ุงูŠุดุŸ ุงู„ X ุนุจุงุฑุฉ ุนู†
237
00:19:45,290 --> 00:19:52,890
ู…ูŠู†ุŸ N times B ู…ุธุจูˆุทุŸ ูŠุนู†ูŠ ุงู„ X ู„ุญุงู„ู‡ุง N times B
238
00:19:52,890 --> 00:19:59,010
ู…ุนุงูƒุฏ ุฃู†ุง ู„ูˆ ุงุฌูŠุช ุถุฑุจุช ูƒู„ ู‡ุฏู N ุจุณุท ู…ู‚ุงู… ุจุทู„ุน
239
00:19:59,010 --> 00:20:07,830
ู…ุนุงุฏูŠ ุงู„ form ู„ุญุงุฌุฉ ุฒูŠ ู‡ูŠ X-NYยฒNY1-Y ู‡ุฐูŠ ูุฑุตุฉ ุฃุฎุฑู‰
240
00:20:07,830 --> 00:20:17,890
ู…ุชุดุงุจู‡ุฉ ู„ู‡ุฐุง ุงู„ู€ Z-score ุงู†ู‡ุง ุชุนุชู…ุฏ ุนู„ู‰ X X-NYยฒNY1
241
00:20:17,890 --> 00:20:21,830
-Y ู‡ุฐู‡ ุงู„ูุฑุตุชูŠู† ู…ุชุดุงุจู‡ุฉ ุจุดูƒู„ ู†ูุณูŠ ู„ุฐุง ูŠู…ูƒู†ูƒ
242
00:20:21,830 --> 00:20:28,460
ุงุณุชุฎุฏุงู… ุงูˆ B-Y ุนุจุฑ ู‡ุฐุง ุงู„ุดุฎุต ู†ุญู† ู†ุญุจ ุงุณุชุฎุฏุงู…ู‡ุฐู‡
243
00:20:28,460 --> 00:20:31,300
ุงู„ููˆุฑู…ูˆู„ุฉ ุฃูˆ ุจุฅู…ูƒุงู†ูƒ ุงุณุชุฎุฏุงู… ุงูƒุณ ู…ุงู†ูˆุณ ุงู† ุจุงูŠ ุนุจุฑ
244
00:20:31,300 --> 00:20:35,760
ุงู† ุจุงูŠ ูˆุงุญุฏ ู…ุงู†ูˆุณ ุจุงูŠ ุงู„ุงุฎุชุตุงุฑุงุช ู‡ู†ุง ุงูƒุณ ุนู„ู‰ ุงู„ุฃู‚ู„
245
00:20:35,760 --> 00:20:42,760
ุฎู…ุณุฉ ูˆุงู† ู…ุงู†ูˆุณ ุงูƒุณ ุนู„ู‰ ุงู„ุฃู‚ู„ ุฎู…ุณุฉ ุงุฐุง ูƒู†ุช ุชู‚ุงุฑู†
246
00:20:42,760 --> 00:20:50,880
ู‡ุฐู‡ ุงู„ุงุฎุชุตุงุฑุงุช ู…ุน ุงู„ุงุฎุชุตุงุฑุงุช ุงู„ุฌุฏูŠุฏุฉ ุงู† ุจูŠ ุนุจุงุฑุฉ
247
00:20:50,880 --> 00:20:56,360
ุนู† ู…ูŠู† ุงูƒุณ ุนู„ู‰ ุงู† ุจูŠ ุนุจุงุฑุฉ ุนู† ู…ูŠู† ุงูƒุณ ุนู„ู‰ ุงู† ุจูŠ
248
00:20:56,360 --> 00:21:01,300
ุนุจุงุฑุฉ ุนู† ู…ูŠู† ุงูƒุณ ุนู„ู‰ ุงู†ู† ุจูŠ ูŠุนู†ูŠ ู‡ุฐู‡ ุตุงุฑุช ู† ุจุงูŠ
249
00:21:01,300 --> 00:21:06,600
ุนุจุงุฑุฉ ุนู† ูƒู„ ุนุจุงุฑุฉ ุนู† x ูˆู‡ุฐู‡ ู„ูˆ ุทู„ุนุชู‡ุง ู‡ุฐู‡ n minus
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n ุจุงูŠ ู…ุด ุดุงูŠู ุงู„ n times n minus ุจุงูŠ ู‡ูŠ n minus ุงู„
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n ุจุงูŠ ุนุจุงุฑุฉ ุนู† ู…ูŠู† ุงู„ู„ูŠ ู‡ูŠ ุงู„ x ู…ู…ูƒู† ุฃุญูƒูŠ ุฅู…ุง x
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ุฃูƒุจุฑ ู…ู† ุณุงุนุฉ ุฎู…ุณุฉ and n minus x at least five or
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ุงู„ู„ูŠ ุญูƒูŠู†ุง ุนู„ูŠู‡ ููŠ ุงู„ุฃูˆู„ n times b ุฃูˆ n times one
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minus b ู‡ุฏูˆู„ุฉ two equivalent formulas either you
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use X minus N by over square root N by one minus Y
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or the previous one which we are familiar with B
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minus Y ุนู„ู‰ square root Y one minus Y over N ุฅุฐุง
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ุจุณุชุฎุฏู… ุฃูŠ ูˆุงุญุฏุฉ ู…ู†ู‡ู… ุงู„ุฃุชู†ูŠู† ุตุญ ู‡ู†ุงุฎุฏ
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example ุนู„ู‰ ู‡ุฐุง ุงู„ู…ูˆุถูˆุน ูˆุญุฏ
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ูŠุฌู„ุณ ุงู„ู…ุซุงู„
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ุฃู…ุงูƒู† ุงู„ู€ company ุจุชุนุฑู ุฃู†ู‡ุง ุชุญุตู„ ุนู„ู‰ 8 ุดุฎุต ูˆ 5
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ู…ุณุชุฎุฏู… ู…ู† ุฎู„ุงู„ ุณู†ุฉ ูŠุนู†ูŠ ููŠ ู‡ุฐุง ุงู„ุจุฑู†ุงู…ุฌ ู…ุฌู…ูˆุนุฉ
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ู…ุฎุชู„ูุฉ ู…ู† 500 ู…ุณุชุฎุฏู… ุงุณุชู‚ุจู„ุช ู…ุน 25 ู…ุณุชุฎุฏู… ุชุณุนุฉ ุฃู„ู
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ูˆุฎู…ุณุฉ ูˆูŠู…ูŠู† ุณู†ุฉ ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู…
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ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู…
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ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู…
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ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู…
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ู…ุณุชุฎุฏู… ู…ุณุชุฎุฏู… ู…ุณุชุดุฑูƒุงุช ู…ุนูŠู†ุฉ ุงูุชุฑุถ ุงู„ response
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ุชุจุนู‡ู… ู…ู…ูƒู† ูŠูƒูˆู† low ูŠุนู†ูŠ ุงู„ู†ุงุณ ู„ู…ุง ุชุณุชุฌูŠุจ ู…ุด ุงู„ูƒู„
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ู‡ูŠุนุจูŠ ุงู„ุงุณุชุฌุงุจุฉ ู…ุด ู‡ูŠูƒ ุงู„ marketing company claims
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that ุชุชุฏุนูŠ ุงู†ู‡ it receives eight percent responses
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from its mailing ู„ู…ุง ุจูŠุจุนุชูˆุง mailing ุจูŠุจุนุชูˆุง ุจุฑูŠุฏ
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ุจูŠุฌูŠู‡ู… ุงู„ุฑุฏ ุจุณ ุชู…ุงู†ูŠุฉ ููŠ ุงู„ู…ูŠุฉ ู…ู† ุงู„ุฑุฏูˆุฏ ูƒู„ู‡ุง to
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test this claim ุนุดุงู† ูŠุฎุชุจุฑูˆุง ู‡ุฐุง ุงู„ุงุฏุนุงุก a random
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sample of 500 were surveyed ูŠุนู†ูŠ ุชู… ุงุณุชุทู„ุงุน ุงูˆ ู…ุณุญ
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ู„ 500 ูˆุงุญุฏ with 25 responses ูˆุงู„ู„ูŠ ุฌุงูˆุจ ู‚ุฏุงุดุŸ 25
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ุฅุฐุง ู‡ูˆ ู‡ูŠุฌุงูˆุจ ุฃูˆ ู…ุด ู‡ูŠุฌุงูˆุจ ูุจุงู„ุชุงู„ูŠ ูƒู„ ูˆุงุญุฏุฉ ุงู„ู„ูŠ
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ู„ู‡ุง two possible outcomes either response or don't
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response ุฎู„ูŠู†ูŠ ุฃุชุทู„ุน ุนู„ู‰ ุงู„ information ุงู„ู„ูŠ
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ู…ูˆุฌูˆุฏุฉ ุนู†ุฏูƒ ููŠ ุงู„ุฃูˆู„ุŒ ุฅูŠุด ุงู„ test ู‡ุชูƒูˆู†ุŸ ู…ูŠูˆ equal
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ูˆู„ุง ุจุงูŠ equalุŸ ู…ู‡ู… ุฌุฏุง ุฃุนุฑู ุฃู†ุง ุจุชูƒู„ู… ุนู„ู‰ ู…ูŠูˆ ูˆู„ุง
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00:23:33,230 --> 00:23:37,890
ุจุงูŠุŸ ุนู„ู‰ ุจุงูŠุŒ ู…ุธุจูˆุท ู„ุฃู† ุฃู†ุง ุจุชูƒู„ู… ุนู„ู‰ ุงู„
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proportion of what we are talking about ุจุงูŠ ุฅุฐุง ุงู„
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ุจุงูŠ equal 8% ุทุจ ูˆ ุงู„ H1ุŸ ู…ุงุญูƒูŠู‡ุงุด ุฃูƒุจุฑ ุฃูˆ ุฃู‚ู„ุŒ
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ู…ุงููŠุด ู…ุนุชุจุฑู‡ุงุŸู„ุงูŠู‡ ู…ุชุณุงูˆูŠุŸ a random sample of size
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500 ู…ุธุจูˆุทุŸ ุฃูƒู…ู„ ูˆุงุญุฏ ุญูƒุงูŠุฉ ุฃูˆ responseุŸ 8x5 ุฃูˆู„ ุดูŠ
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ุจุชุฃูƒุฏ ู…ู† ุงู„ two conditions ุงู„ู„ูŠ ุนู†ุฏู‰ ุงู„ู„ูŠ ู‡ูŠ n
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times y 500 times 8 ู„ูˆ ุถุฑุฑุช 5 ููŠ 8 ุจุทู„ุน ุงู„ 40 ุทุจ ูˆ
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n times 1 minus y ู…ู† ุบูŠุฑ ู…ุญุณุจุฉ ู…ุด ู…ุชุณุงูˆูŠุŸุงู„ู„ูŠ ู‡ูŠ n
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times one minus pi ู…ู† ุบูŠุฑ ู…ุง ู†ุญุณุจู‡ุง ุงู„ู„ูŠ
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ู‡ูŠ ุงู„ complement ู„ู„ุฎู…ุณู…ูŠุฉ ู…ุธุจูˆุท ู…ูƒู…ู„ ุงู„ุฎู…ุณู…ูŠุฉ ุงุฐุง
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ูƒุงู† ุฏูˆู„ุฉ ุงุฑุจุนูŠู† ูˆุนู†ุฏูŠ ุฎู…ุณูŠู† ูˆุทู„ุน ุงุฑุจุน ู…ูŠุฉ ูˆุณุชูŠู† ู„ูˆ
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ุจุชุญุณุจูŠู‡ุง I ุฎู…ุณู…ูŠุฉ of one minus pi ูŠุนู†ูŠ ุฎู…ุณู…ูŠุฉ ููŠ
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ุงุชู†ูŠู† ูˆุชุณุนูŠู† ุงู„ู„ูŠ ู‡ูŠ ุงุฑุจุน ู…ูŠุฉ ูˆุณุชูŠู† ูˆุงุถุญ ุฃู† ู‡ุคู„ุงุก
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ุงู„ุงุชู†ูŠู† ู„ูˆ ุฌู…ุนู†ุงู‡ ู…ุด ุจูŠุทู„ุน ุงู„ุฌูˆุงุจ ู…ู„ูŠุงู†ุฉ
296
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ู…ุงููŠุด ุฏู„ูˆู‚ุชูŠ ุฃู† ุฃุถุฑุจู‡ุง ู…ู…ูƒู† ุฃุทู„ุน ุงู„ุฌูˆุงุจ ุนู„ู‰ ุทูˆู„
297
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ุฅุฐุง ูˆุงุถุญ ุงู„ conditions ู…ุง ู„ู‡ู… are satisfied
298
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because the conditions are n times pi at least 5
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and n times 1 minus pi is at least 5 in this case
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we got 40 and 406 it means the two conditions are
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okay ุงู„ุงู† ูŠุฌุจ ุฃู† ู†ุฌุฏ ู‚ูŠู…ุฉ ู…ู‡ู…ุฉ ุณุฃู‚ูˆู…
302
00:25:28,000 --> 00:25:35,280
ุจุนู…ู„ ุงู„ู…ุดูƒู„ุฉ ุจุงุณุชุฎุฏุงู… ู‚ูŠู…ุฉ ู…ู‡ู…ุฉ ู‚ุฑูŠุจุฉ ุซู… ุจุงุณุชุฎุฏุงู…
303
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ู‚ูŠู…ุฉ P ู‚ุฑูŠุจุฉ ุงู„ุฃู† Alpha 5% ู†ุญู† ู†ุชูƒู„ู… ุนู† ุชุฌุงุฑุจ 2D
304
00:25:48,680 --> 00:25:51,180
ู‡ู†ุง ูŠูˆุฌุฏ ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช
305
00:25:51,180 --> 00:25:52,260
ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช
306
00:25:52,260 --> 00:26:01,660
ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช ุงุชุฌุงุฑุงุช
307
00:26:05,360 --> 00:26:09,440
ู„ุฐู„ูƒ ุงู„ู…ู†ุงุทู‚ ุงู„ุงู†ุชู‚ุงู„ูŠุฉ ุฃูƒุชุฑ ู…ู† 1.96 ุฃูˆ ุฃูƒุชุฑ ู…ู†
308
00:26:09,440 --> 00:26:15,360
ู†ู‚ู„ 1.96 ุฅุฐุง ูƒุงู†ุช ู‚ูŠู…ุฉ ุงู„ุงู†ุชู‚ุงู„ูŠุฉ ุชุณู‚ุท ููŠ ู‡ุฐู‡
309
00:26:15,360 --> 00:26:18,520
ุงู„ู…ู†ุงุทู‚ ุงู„ุงู†ุชู‚ุงู„ูŠุฉ ุฅู„ู‰ ุงู„ูŠุณุงุฑ ุฃูˆ ุงู„ูŠุณุงุฑุŒ ูุณู†ู†ู‚ู„
310
00:26:18,520 --> 00:26:24,200
ุฅู„ู‰ ุงู„ู‡ูŠุจูˆุช ู†ูุณูŠ ุฏุนูˆู†ุง ู†ุญูƒู… ููŠ ู‡ุฐู‡ ุงู„ุงู†ุชู‚ุงู„ูŠุฉ
311
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b-y over square root of y 1-y over n ุจูŠุฒ ุงูƒุณ over
312
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n ุจูŠุฒ ุงูƒุณ
313
00:26:42,350 --> 00:26:44,890
ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ
314
00:26:44,890 --> 00:26:45,430
ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ
315
00:26:45,430 --> 00:26:48,230
ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ
316
00:26:48,230 --> 00:26:50,130
ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ
317
00:26:50,130 --> 00:26:50,170
ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ ุนุดุฑ
318
00:26:50,170 --> 00:26:54,310
ุนุดุฑ
319
00:26:54,310 --> 00:26:59,350
ุนุดุฑ
320
00:26:59,350 --> 00:27:07,050
ุนุงู„ู„ูŠ ู‡ูŠ square root of pi 1 minus pi over n ุงู„ู„ูŠ
321
00:27:07,050 --> 00:27:15,330
ู‡ูŠ 8 percent 92 percent over 500 ู…ู…ูƒู† ุชุญุณุจูŠู‡ุง ุฃู†ุง
322
00:27:15,330 --> 00:27:19,870
ุจูุถู„ ุฃุญุณุจู‡ุง ูˆุจุนุฏูŠู† ุฃุญุทู‡ู… ููŠ ุงู„ู…ุนุงุฏู„ุฉ ุงู„ู„ูŠ ู‡ูŠ
323
00:27:19,870 --> 00:27:24,690
point
324
00:27:24,690 --> 00:27:27,810
zero nine eight times nine
325
00:27:31,420 --> 00:27:39,380
ุฅุฐุง ุจุงู„ู€ 0.8 ูŠุนู†ูŠ 0.92 ุชู‚ุณูŠู… 500 ุจุทู„ุน ุงู„ square
326
00:27:39,380 --> 00:27:43,560
root 001472
327
00:27:43,560 --> 00:27:47,980
ู„ูˆ
328
00:27:47,980 --> 00:27:53,420
ุทู„ุนู†ุง ุงู„ square root 0
329
00:27:53,420 --> 00:27:56,540
.0001472
330
00:27:56,540 --> 00:28:03,390
ุฅูŠุด ุจุทู„ุน ุงู„ุฌูˆุงุจุŸ ุจุชุทู„ุน ุฌูˆุงุจ ู‡ุฐุง ุงู„ู€ square root
331
00:28:03,390 --> 00:28:13,370
ู„ู„ู‚ูŠู…ุฉ ู‡ุฐู‡ ุงู„ู„ูŠ
332
00:28:13,370 --> 00:28:18,730
ู‡ูŠ point zero zero one four seven two ุจุชุทู„ุน ุฌูˆุงุจ
333
00:28:18,730 --> 00:28:26,630
ูƒุฏู‡ุŸ zero one two ุชู‚ุฑูŠุจุง ุญุณุงุจ ุงู„ุชุฏูˆู„ุŸ ุฅุฐุง ุฃู†ุง ุจู†ุตุญ
334
00:28:26,630 --> 00:28:31,170
ุฏู‡ ู…ู† ุฃุนู…ู„ ุฒูŠ ู‡ูŠูƒ ุฃุทู„ุน ุงู„ b ูˆ ุงู„ sigma ู„ู„ b ูˆ
335
00:28:31,170 --> 00:28:35,110
ุจุนุฏูŠู† ุฃุญุณุจ ุงู„
336
00:28:35,110 --> 00:28:42,250
z set ุจุชุณุงูˆูŠ b minus pi ุน sigma ู„ู„ b ุงู„ b 5
337
00:28:42,250 --> 00:28:47,490
percent ุงู„ pi ุจู‚ูŠุช ุงู„ sigma ู„ู„ b ุฃู†ุง ุฃุทู„ุนู‡ุง ุชู‚ุฑูŠุจุง
338
00:28:47,490 --> 00:28:51,730
0.12 ุงู„ุฌูˆุงุจ ุทุงู„ุน negative 2.47
339
00:28:59,160 --> 00:28:59,600
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
340
00:28:59,600 --> 00:29:07,040
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
341
00:29:07,040 --> 00:29:09,020
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
342
00:29:09,020 --> 00:29:09,760
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
343
00:29:09,760 --> 00:29:10,160
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
344
00:29:10,160 --> 00:29:10,440
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
345
00:29:10,440 --> 00:29:10,500
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
346
00:29:10,500 --> 00:29:10,780
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
347
00:29:10,780 --> 00:29:23,220
ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง ุฅุฐุง
348
00:29:26,930 --> 00:29:31,270
-2.47% ู…ูˆุฌูˆุฏุฉ ููŠ ู‡ุฐู‡ ุงู„ู…ุฌุงู„ ุงู„ุชุฑูุถ ูˆุงุถุญ ุงู† ู‚ูŠู…ุฉ
349
00:29:31,270 --> 00:29:36,190
ุงู„ุญุตุงุก ูˆูŠู† ู…ูˆุฌูˆุฏุฉ ููŠ ู…ู†ุทู‚ุฉ ุงู„ุฑูุถ ุชู‚ูˆู„ ู†ุญู† ู†ุชูุฑุฌ ุนู†
350
00:29:36,190 --> 00:29:40,830
ุงู„ู€ null hypothesis ุทุงู„ู…ุง ู†ุชูุฑุฌ ุนู† ุงู„ุงุฎุชุตุงุฑ ูŠูˆุฌุฏ
351
00:29:40,830 --> 00:29:45,990
ูˆุซู‚ุฉ ูƒุงููŠุฉ ู„ุชูุฑุฌ ุนู„ู‰ ุงุนุชุจุงุฑ ุงู„ุดุฑูƒุงุช ู…ู† 8% ุนุฏุฏ
352
00:29:45,990 --> 00:29:50,550
ุงู„ุฅุฌุงุจุฉ ุฅุฐู† ู‡ู…ุง ูƒุงู†ูˆุง ุฏุนุงู‡ู… ุฅู†ู‡ ู„ู… ูŠุฌูŠุจูˆุง 8%
353
00:29:50,550 --> 00:29:55,370
ูƒู„ุงู…ุชู‡ ุตุญ ูˆู„ุง ุบู„ุท ู…ุด ุตุญุŸ ุจุงู„ุชุงู„ูŠ ู‡ูˆ ู…ุงู„ู‡ differs
354
00:29:55,370 --> 00:29:59,190
from 8% do you think it's smaller than or greater
355
00:29:59,190 --> 00:30:04,350
than 8%ุŸ ู„ูˆ ุทู„ุน ุงู„ conclusion ุชูƒูˆู† ุจุงูŠ ุฃูƒุจุฑ ูˆู„ุง
356
00:30:04,350 --> 00:30:09,810
ุฃู‚ู„ุŒ ุฅูŠุด ุชุชูˆู‚ุนูŠุŸ ู…ุง ู‡ูŠ ู„ุง ูŠุชุณุงูˆู‰ ู…ุนู†ุงู‡ุง ูˆุงุญุฏุฉ ู…ู†
357
00:30:09,810 --> 00:30:15,050
ุงู„ุฃุชู†ูŠู† ู„ุง ูŠุชุณุงูˆู‰ ู…ุนู†ุงู‡ุง .. ุฃู†ุง ุจุญูƒูŠู„ูƒ ุฃู†ุช ู…ุงุญูƒูŠุด
358
00:30:15,050 --> 00:30:18,470
ุนุดุฑ ุฃุดูŠุงุก ู…ุงุญูƒูŠุด ู…ุนู†ุงู‡ุง ูŠุง ู…ุนุงูƒ ุฃูƒุชุฑ ูŠุง ู…ุนุงูƒ ุฃู‚ู„
359
00:30:18,470 --> 00:30:21,850
ุทูŠุจ ู‡ูŠู† .. ู„ู…ุง ุจุญูƒูŠ ู…ุนุงูƒ .. ุงู„ buy ุจุชุณุงูˆูŠุด ุฎุงู† 8%
360
00:30:22,650 --> 00:30:28,010
ู…ุนู†ุงู‡ ุฃูƒุจุฑ ูˆู„ุง ุฃู‚ู„ ููŠ ุงู„ุญุงู„ุฉ ุชุจุนุชู†ุงุŸ ู„ูŠุด ุฃูƒุจุฑุŸ
361
00:30:28,010 --> 00:30:32,870
ุนุดุงู† ุงู„ุณู„ุฉ ุจุชูƒูˆู† ุฃูƒุจุฑุŸ ู„ู…ุง ุงู„ุดู„ุฉ ุชูƒูˆู† ุงู„ุณู„ุฉ ุจุชูƒูˆู†
362
00:30:32,870 --> 00:30:36,770
ุฃูƒุจุฑ ูˆู„ุง ุฃู‚ู„ุŸ ู„ู…ุง ูŠูƒูˆู† ุนู†ุฏูƒ ุฌูˆุงุจ ุจุงู„ negative
363
00:30:36,770 --> 00:30:40,610
ุจุชูƒูˆู† ุงู„ู‚ูŠู… ุฃูƒุจุฑ ูˆู„ุง ุฃู‚ู„ุŸ ุงู†ุช ู„ุญุธุฉ ุทุงู„ุน ุฃู†ุช
364
00:30:40,610 --> 00:30:45,570
ู…ุงุญุชูุธุด ู…ู† ุนู†ุฏูƒ ุจูŠ minus ุจุงูŠ negative ู…ุน ูƒุฏู‡ ุงู„ุจูŠ
365
00:30:45,570 --> 00:30:50,430
ุฃู‚ู„ ูˆู„ุง ุฃูƒุจุฑ ู…ู† ุจุงูŠุŸ ุฃู‚ู„ ู…ู† ุจุงูŠุช ูุจุชุฎูŠู„ ุจุงุณู†ุชุฌุฑ
366
00:30:50,430 --> 00:30:52,950
ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช
367
00:30:52,950 --> 00:30:56,370
ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง
368
00:30:56,370 --> 00:30:56,830
ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู†
369
00:30:56,830 --> 00:30:56,910
ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู†
370
00:30:56,910 --> 00:31:04,750
ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„ ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง ุฃู‚ู„
371
00:31:04,750 --> 00:31:10,050
ู…ู† ุจุงูŠุช ุชุนุชู…ุงู„ู‡ุง
372
00:31:10,050 --> 00:31:16,290
ุฃู‚ู„
373
00:31:16,290 --> 00:31:25,660
ู…ู† ุจุงูŠุช ุงู„ู€ P-Value ุฏุนูˆู†ูŠ ุฃุฑู‰ ู…ุน ุจุนุถ ู‡ุฐุง ู‡ูˆ
374
00:31:25,660 --> 00:31:30,500
P-Value P-Value ุณุชุณุงูˆูŠ ุฅุฐุง ุฑุฃูŠุช ุงู„ู€ Statistics
375
00:31:30,500 --> 00:31:37,460
ูŠูƒูˆู† ุฃูƒุจุฑ ู…ู† ุงู„ู‚ูŠู…ุฉ ุฃูˆ ุฃุตุบุฑ ู…ู†ู‡ุง ูŠุนู†ูŠ ุณุฃุฎุฏ ู‚ุทุน ุงู„ู€
376
00:31:37,460 --> 00:31:43,820
Absolute Value Z ุฃูƒุจุฑ ู…ู† 2 ุฃูˆ Z ุฃู‚ู„ ู…ู† negative 2
377
00:31:43,820 --> 00:31:48,780
.47 ุงู„ุชูŠู†ุชูŠู† ุฒูŠ ุจุนุถุŒ ู…ุธุจูˆุท ุฏุงูŠู…ุง .. ู‡ุฏูˆู„ ุฏุงูŠู…ุง ุฎู„ูŠ
378
00:31:48,780 --> 00:31:54,720
ุจุงู„ูƒ .. ู„ู…ุง ุจุชูƒู„ู… ุนู† ุงู„ B value ุจุญุท ู‡ู†ุง ู…ูŠู† ุงู„ Z
379
00:31:54,720 --> 00:31:59,960
statistic ุญูƒูŠุช ุฏูŠ ุนุงู…ุฉ ุดูˆูŠุฉ ูุจุงู„ุชุงู„ูŠ ู‡ุชูƒูˆู† 2.47
380
00:31:59,960 --> 00:32:04,180
ู‡ู†ุง ูˆู‡ู†ุง negative 2.47 ุงู„ุชูŠู†ุชูŠู† ู‡ุฏูˆู„ ุฒูŠ ุจุนุถุŒ
381
00:32:04,180 --> 00:32:08,080
ู…ุธุจูˆุท ุจุทู„ุน ูˆุงุญุฏุฉ ุจุถุฑุจ ููŠ ุงุชู†ูŠู† ู…ูŠู† ู„ุณู‡ ู„ุทู„ุนุŸ
382
00:32:08,080 --> 00:32:12,950
ุงู„ุฃูƒุจุฑ ูˆู„ุง ุงู„ุฃู‚ู„ุŸ ุฏุงูŠู…ุง ุงู„ุฃุณู„ุฉ ุญุณุจ ุงู„ table ุงู„ุชูŠุจู„
383
00:32:12,950 --> 00:32:15,750
ุงู„ู„ูŠ ุนู†ุฏูƒ ู…ูŠุนุทูŠ ู…ุณุงุญุฉ ูŠู…ูŠู† ูˆู„ุง ุดู…ุงู„ ุชุจู‚ู‰ ุงู„ Z ุชุจู‚ู‰
384
00:32:15,750 --> 00:32:21,490
ุงู„ Z ุฎู„ูŠ ุจุงู„ูƒ ู‡ุฐุง Z ู‡ุฐุง ุงู„ุชูˆุฒูŠุน Z ู…ุด T ุฒูŠ ุงู„ู„ูŠ
385
00:32:21,490 --> 00:32:25,130
ูุงุช ุงู„
386
00:32:25,130 --> 00:32:29,530
negative ุฃูŠู‡ ุฌุงู‡ุฒ ุจูŠุนุทูŠู†ุง ุฅูŠู‡ to the right ูˆ to
387
00:32:29,530 --> 00:32:34,790
the left ุจุงู„ุชุงู„ุฉ ุฏูŠ ุฌุงู‡ุฒุฉ ุงู„ู„ูŠ ุฃูƒุจุฑ ุจุฏูŠ ุฃุนู…ู„ one
388
00:32:34,790 --> 00:32:38,910
minus ู…ุด ุดูƒ ุงู„ุงุชู†ูŠู† ุตุญ ูุจุฃุฎุฏ ูˆุงุญุฏุฉ ู…ู†ู‡ู… ูˆ ุจุถุฑู
389
00:32:38,910 --> 00:32:43,450
ุงู„ุงุชู†ูŠู† ุฎุฏ ุฃูŠ ูˆุงุญุฏุฉ ู…ู†ู‡ู… ุฃู†ุง ุจุฏูŠ ุฃุฎุฏ ุงู„ุฃุณู‡ู„ุงู„ู„ูŠ
390
00:32:43,450 --> 00:32:51,310
ุฌุงู‡ุฒุฉ ุนู†ุฏู‰ negative 2.4 under 7 ู‡ูŠ negative 2.4
391
00:32:51,310 --> 00:32:54,350
0068
3