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Magazine Problem 51
Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance \(\alpha\). Right-tailed test, \(n=20, \alpha=0.05\)
Problem 52
Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance \(\alpha\). Two-tailed test, \(n=14, \alpha=0.01\)
Problem 55
Test the claim about the population variance \(\sigma^{2}\) or standard deviation \(\sigma\) at the level of significance \(\alpha\). Assume the population is normally distributed. Claim: \(\sigma^{2}>2 ; \alpha=0.10\). Sample statistics: \(s^{2}=2.95, n=18\)
Problem 56
Test the claim about the population variance \(\sigma^{2}\) or standard deviation \(\sigma\) at the level of significance \(\alpha\). Assume the population is normally distributed. Claim: \(\sigma^{2} \leq 60 ; \alpha=0.025\). Sample statistics: \(s^{2}=72.7, n=15\)
Problem 57
Test the claim about the population variance \(\sigma^{2}\) or standard deviation \(\sigma\) at the level of significance \(\alpha\). Assume the population is normally distributed. Claim: \(\sigma=1.25 ; \alpha=0.05\). Sample statistics: \(s=1.03, n=6\)
Problem 58
Test the claim about the population variance \(\sigma^{2}\) or standard deviation \(\sigma\) at the level of significance \(\alpha\). Assume the population is normally distributed. Claim: \(\sigma \neq 0.035 ; \alpha=0.01\). Sample statistics: \(s=0.026, n=16\)
Problem 59
(a) identify the claim and state \(H_{0}\) and \(H_{a}\), (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic \(\chi^{2}\), (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. A bolt manufacturer makes a type of bolt to be used in airtight containers. The manufacturer claims that the variance of the bolt widths is at most \(0.01\). A random sample of 28 bolts has a variance of \(0.064\). At \(\alpha=0.005\), is there enough evidence to reject the claim?
Problem 60
(a) identify the claim and state \(H_{0}\) and \(H_{a}\), (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic \(\chi^{2}\), (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. A restaurant claims that the standard deviation of the lengths of serving times is 3 minutes. A random sample of 27 serving times has a standard deviation of \(3.9\) minutes. At \(\alpha=0.01\), is there enough evidence to reject the claim?
