Order the following $p$-values from the weakest to the strongest evidence against the null hypothesis ($H_0$):

1. $p=0.045$

2. $p=0.510$

3. $p=0.001$

4. $p=0.125$

A poll suggests that over $75\%$ of city residents support expanding public transportation. In a random sample of $60$ residents, $78\%$ expressed support. At $\alpha =0.05$, is there sufficient evidence to back the poll's claim?

A company advertises that at least $70\%$ of its customers are satisfied with their service. In a survey of $150$ customers, $99$ say they are satisfied. Which of the following is the correct null hypothesis for testing the company's claim?

A workforce analyst claims that more than half of remote employees believe their time management skills improved while working from home. In a random sample of $280$ remote employees, $158$ say their time management skills improved. At the $0.01$ significance level, is there enough evidence to support the analyst’s claim?

A health organization surveyed $950$ adults about flu vaccination. The organization stated that $60\%$ of all adults received a flu shot, with a margin of error of $3.5\%$ at a $95\%$ confidence level. What inference can be made from this survey?

A survey analyst claims that at least $60\%$ of consumers support stricter labeling laws for organic products. A recent random sample of $180$ consumers shows that $102$ of them support stricter labeling laws. Using a significance level of $\alpha =0.10$, is there enough evidence to reject the analyst’s claim?

A local haunted house claims that at least $60\%$ of its visitors report being scared during the tour. A skeptical blogger suspects the true proportion is less than $60\%$, and collects a random sample of $50$ visitors, of whom $25$ said they were scared. Use a randomization procedure to test the blogger's claim at the $0.05$ significance level.

Consider a hypothesis test for the proportion of a population, where the test statistic obtained is $z=-1.45$. The claim being tested is that the population proportion is greater than $0.4$.

i. Determine whether the test is two-tailed, right-tailed, or left-tailed.

ii. Calculate the $p$-value for this test.

iii. At a significance level of $\alpha =0.05$, should we reject the null hypothesis or fail to reject it?

A survey of $1800$ college students found that $38\%$ said they prefer online classes over in-person classes. Test the claim, at the $0.01$ significance level, that fewer than half of college students prefer online classes.

A researcher claims that $40\%$ of adults exercise at least three times a week. In a survey of $500$ adults, $215$ said they exercise at least three times a week. At the $0.01$ significance level, test the researcher's claim.