91Ó°ÊÓ

The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\). $$p \leq 0.4$$

Find the \(P\)-value for the hypothesis test with the standardized test statistic z. Decide whether to reject \(H_{0}\) for the level of significance \(\alpha\). Left-tailed test, \(z=-1.18, \alpha=0.05\)

Find the critical value(s) and rejection region(s) for the type of \(z\)-test with level of significance \(\alpha\). Include a graph with your answer. Left-tailed test, \(\alpha=0.02\)

(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 \(z\), (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. An environmental researcher claims that the mean amount of sulfur dioxide in the air in U.S. cities is \(1.15\) parts per billion. In a random sample of 134 U.S. cities, the mean amount of sulfur dioxide in the air is \(0.93\) parts per billion. Assume the population standard deviation is \(2.62\) parts per billion. At \(\alpha=0.01\), is there enough evidence to reject the claim? (Source: U.S. Environmental Protection Agency)

(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 \(t\), (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 fitness magazine claims that the mean cost of a yoga session is no more than \(\$ 14\). You want to test this claim. You find that a random sample of 32 yoga sessions has a mean cost of \(\$ 15.59\) and a standard deviation of \(\$ 2.60\). At \(\alpha=0.025\), do you have enough evidence to reject the magazine's claim?

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, \(n=14, \alpha=0.01\)

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: \(s=0.026, n=16\)

(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?