2. Consider the population of ALL the pennies in the U.S. Suppose that you want to learn about the mean age ALL pennies but you can only afford to take a sample of 25 pennies. Assume that the ages of pennies are approximately normally distributed with = 6.23 years.

Pennies: 2011, 2011, 2006, 1990, 1983, 2008, 1981, 2017, 2018, 2012, 2018, 1980, 2007,2004, 1968, 2016, 1992, 2012, 1995, 2018, 2016, 1987, 1987, 1989, 1988 a. Assume that the 25 pennies in your bag is a random sample from all pennies. Record the age of the pennies (subtract the year it was made from 2022). Then calculate the mean of the ages. b. Is this mean you calculated in part (a) a parameter or a statistic? What symbol represents it? c. Do you know the value of the mean age of pennies in your sample? If so, what's that value? d. Is the mean age of all pennies a parameter or a statistic? What symbol represents it? e. Do you know the value of mean age of all pennies? If so, calculate it. f. Clearly the students in this class will get many different values for their sample mean. What statistical term refers to this phenomenon? g. Check the conditions for calculating the confidence interval. Are the ages of all pennies normally distributed? Or is > 30?

h. Construct a 95% confidence interval using the sample values to estimate the mean age of all pennies. i. Write the correct in-context interpretation of this interval in words (refer back to your notes). j. What is the margin of error of your confidence interval? k. How many pennies should we have in our sample if we want the margin of error to be half of what you got in part j? l. What percent of all of the calculated 95% confidence intervals should contain the population parameter? m. Would the 99% confidence interval be wider or narrower? n. If we had 15 pennies in our sample instead of 25, would the 95% confidence interval wider or narrower?

o. Suppose that the mean age of all pennies is 18.6 years. Is this value in your confidence interval? p. We want to test the claim that the mean age of all pennies is 18.6 years. Write the null and alternative hypothesis for the test. Use a two-sided test. q. Are the conditions for the hypothesis test satisfied? r. Find the test statistic. Draw the sampling distribution and shade the appropriate area(s). s. Find the -value using your z-table. t. Write your conclusion in context. u. If the true age of all pennies is not 18.6 years but we do not reject this hypothesis, then what type oferror did we make?