1. In a simple random sample of 144 households, the sample mean number of personal computers was 1.28. Assume the population standard deviation is 0.36.

a)(6 points)Construct a 95% confidence interval for the mean number of personal computers.

b)(2 points)If the sample size were 121 rather than 144, would the margin of error be larger or smaller than the result in part (a)? Explain.

10.(7 points)A study by the Web metrics firm Experian showed that in August 2011, the mean time spent per visit to Facebook was 20.8 minutes. Assume the standard deviation is 6 minutes. Suppose that a simple random sample of 225 visits in August 2013 has a sample mean of 23 minutes. A social scientist is interested to know whether the mean time of Facebook visits has increased. Perform an appropriate hypothesis test with = 0.05level of significance.

11.(8 points)A manager of a grocery store needs to manage the number of customers in his store to maintain safe conditions during the pandemic. He takes the following measurements of the customers in the store: 120 150 110 100 80 140 130 120

Assuming that the population is approximately normal, construct a 95% confidence interval for the population mean.