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?

In a study of users’ adoption of a new app feature, researchers claim that the true adoption rate $p$ is greater than $30\%$. They collect a sample of $n=100$ users and find a sample proportion $\hat{p}=0.35$. At $\alpha =0.05$, can they use the normal approximation, and do the data support the claim?

A researcher claims that the proportion of defective items produced by a machine is $0.12$. In a random sample of $20$ items, $5$ are found to be defective. Using the exact binomial method, what is the P-value for testing the alternative hypothesis $H_a:p>0.12$? Use a significance level of $0.05$.

A wildlife research group surveyed a sample of individuals about their experiences with birdwatching. Participants were asked whether they had ever seen a rare bird in the wild. The results are shown in the table below:

Test the claim that gender is independent of having seen a rare bird using a $0.01$ significance level. Does the conclusion change if the significance level is instead $0.05$?

A health newsletter asserts that $15\%$ of residents in County B smoke cigarettes. What is the minimum required sample size ($n$) to estimate this proportion with a $95\%$ confidence interval with a margin of error ($E$) of $0.03$, using the claimed proportion as the planning value?