1. A person randomly selected four bags of carrots (each labeled 20 pounds) and weighed the bags.They weighed 20.5, 19.8, 20.8, and 20.0 pounds.Assume that the distribution of the population is Normal.

A. Construct the 95% confidence interval to estimate the mean weight of all bags of carrots.

B. Is there evidence to reject the claim that the mean weight of all bags of carrots are 20 pounds?

C. Find the 90% confidence interval using the same sample data.

D. Which confidence interval is wider: the 95% interval or the 90% interval?

2. About 35% of U.S. adults said they personally owned stocks, bonds or mutual funds outside of retirement accounts in aPew Research Center surveyfrom September 2019.

Suppose we randomly select 500 adults from the state of Michigan and we want to know if adults in Michigan are more likely to own stocks, bonds, or mutual funds outside of retirement accounts. To find out, we will run a hypothesis test at a significance level of = 0.05. Of the 500 people in the sample, 196 owned stocks, bonds, or mutual funds outside of retirement accounts.

A) State the null and alternative hypothesis.

B) Calculate the standard error.

C) Find the test-statistic and p-value.

D) What does the p-value mean in context? Answer in complete sentences.

E) State the test decision.

F) What is your conclusion in context?