To test (H_{0}: sigma=50) versus (H_{1}: sigma <50), a random sample of size (n=24) is obtained from

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To test $H_{0}: \sigma=50$ versus $H_{1}: \sigma<50$, a random sample of size $n=24$ is obtained from a population that is known to be normally distributed.

(a) If the sample standard deviation is determined to be $s=47.2$, compute the test statistic.

(b) If the researcher decides to test this hypothesis at the $\alpha=0.05$ level of significance, determine the critical value.

(c) Draw a chi-square distribution and depict the critical region.

(d) Will the researcher reject the null hypothesis? Why?

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Statistics Informed Decisions Using Data

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Authors: Michael Sullivan

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To test (H_{0}: sigma=50) versus (H_{1}: sigma <50), a random sample of size (n=24) is obtained from

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