From a Congressional Research Service (Updated Sept. 13, 2019) on The Social Security Retirement Age: The Social Security full retirement age (FRA) is the age at which workers can first claim full Social Security retired-worker benefits. Currently, the FRA is 66 and 6 months (66.5 years of age) for workers who become eligible for retirement benefits in 2019 (i.e., workers born in 1957). Claiming benefits before the FRA results in a permanent reduction in monthly benefits (to take into account the longer expected period of benefit receipt); claiming benefits after the FRA results in a permanent increase in monthly benefits (to take into account the shorter expected period of benefit receipt). A random sample of 20 retirees in 2019 was collected and the age in years at which they retired was recorded in the data set Retirement Age. Using = 0.01, is there sufficient evidence to conclude the average age of 2019 retirees is different from the FRA of 66.5 years? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. Use the research question to define the population parameter in context in one sentence. State the null and alternative hypotheses using correct notation and state the significance level for this problem. Determine if you can complete this problem and which distribution you can use (z or t) to conduct this hypothesis test by checking all conditions. Create a QQ Plot, a histogram, and a box plot of the sample data and present the graphs in your document if necessary. Calculate the test statistic by-hand. First, calculate the sample mean and sample standard deviation using StatCrunch or R and do not round these values. Next, show the work necessary to obtain the test statistic by typing all your steps and providing the resulting test statistic. Do not round anything during the calculation. Then, round the test statistic to three decimal places after you complete the calculation. Use StatCrunch or R to verify your test statistic. Copy and paste this box into your document. Produce a rejection region and copy it into your document. State the p-value and the degrees of freedom using the output provided. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. Construct a 99% confidence interval using StatCrunch or R. Copy the output into your document as your answer. Use the confidence interval to verify the decision you made in your hypothesis test.

data set

Age of Retirement var2 63.6 "" 52.8 "" 61.2 "" 60.1 "" 56.9 "" 55.5 "" 65.1 "" 63.3 "" 74.8 "" 79.7 "" 51.4 "" 49 "" 64.2 "" 56.8 "" 74.5 "" 58.9 "" 77.8 "" 60.3 "" 66.5 "" 68.7 "" "" "" "" ""