A Summary of Hypothesis Testing 403 Chi-Square Test for a Hypothesized Variance S 2 or Standard Deviation S (Section 7.5) Test statistic: s2 Standardized test statistic: x 2 Critical value: x 2 0 (Use Table 6.) Sampling distribution is approximated by a chi-square distribution with d.f. = n - 1. χ2 0 χ2 α α χ2 L χ2 R χ2 1 2 α 1 2 α χ2 0 χ2 Left-Tailed Two-Tailed Right-Tailed x 2 = 1n - 12s2 s 2 Sample variance Hypothesized variance Sample size t@Test for a Hypothesized Mean M (S Unknown) (Section 7.3) Test statistic: x Standardized test statistic: t Critical value: t0 (Use Table 5.) Sampling distribution of sample means is approximated by a t@distribution with d.f. = n - 1. t 0 α t 0 t 0 α −t 0 t 0 1 2 α 1 2 t 0 t 0 α Left-Tailed Two-Tailed Right-Tailed t = x - m s 1n Hypothesized mean Sample standard deviation Sample size Sample mean z@Test for a Hypothesized Mean M (S Known) (Section 7.2) Test statistic: x Standardized test statistic: z Critical value: z0 (Use Table 4.) Sampling distribution of sample means is a normal distribution. z 0 α z 0 z 0 α −z 0 z 0 1 2 α 1 2 z 0 z 0 α Left-Tailed Two-Tailed Right-Tailed z@Test for a Hypothesized Proportion p (Section 7.4) Test statistic: np Standardized test statistic: z Critical value: z0 (Use Table 4.) Sampling distribution of sample proportions is a normal distribution. z = x - m s 1n Hypothesized mean Population standard deviation Sample size Sample mean Hypothesized proportion Sample size z = np - p 2 pq n q = 1 - p Sample proportion Study Tip When your standardized test statistic is z or t, remember that these values measure standard deviations from the mean. Values that are outside of {3 indicate that H0 is very unlikely. Values that are outside of {5 indicate that H0 is almost impossible.
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