Question4. In a simple random sample of 1500 young people, $76 \%$ had earned a high school diploma. Suppose this sample is used to find that the $95 \%$ confidence interval for the the past, 7 of young people who have earned a high school diploma is $(0.738,0.782)$. In confidence of all young people earned high school diplomas. Does the given earn high school diplomas hasdecreased? Explain. 15 claim hypothesis support the true the given enfidence interval suppor the claim that the percentaye has decreased $76 \%$. thein yh the past $79 \%$. of all young people.
3. The U.S. Department of Health has suggested that a healthy total cholesterol measurement should be $200 \mathrm{mg} / \mathrm{dL}$ or less. Records from 50 randomly and independently selected people from a study showed a sample mean of $208.61 \mathrm{mg} / \mathrm{dL}$ and a standard deviation of $39.52 \mathrm{mg} / \mathrm{dL}$. Test the hypothesis that the mean cholesterol level is more than $200 \mathrm{mg} / \mathrm{dL}$ using a significance level of 0.05 . a) Clearly state the null and alternative hypotheses for the test. (4 pts) $$\begin{array}{l} H_{0}: u=200 \\ H_{A}: u>200 \mathrm{~V} \end{array}$$ b) Technology output for the test is given below. State the $t$-stat and $p$-value (Round to 3 decimal places). (2 pts) c) Based on your results from part (b) will you reject the null hypgthesis or not? Explain why or why apo. ( 4 pts ) (5 pls) d) Write a sentence clearly stating your conclusion in the context of the problem.