Question

one year, the mean age of an inmate on death row was 40.1 years. a sociologist wondered whether the mean age of a death - row inmate has changed since then. she randomly selects 32 death - row inmates and finds that their mean age is 38.3, with a standard deviation of 9.3. construct a 95% confidence interval about the mean age. what does the interval imply? click the icon to view the table of critical t - values. ( h_1mu
eq40.1 ) (type integers or decimals. do not round.) construct a 95% confidence interval about the mean age. with 95% confidence, the mean age of a death row inmate is between 34.95 years and 41.65 years. (round to two decimal places as needed.) what does the interval imply? a. since the mean age from the earlier year is contained in the interval, there is sufficient evidence to conclude that the mean age had changed. b. since the mean age from the earlier year is not contained in the interval, there is not sufficient evidence to conclude that the mean age had changed. c. since the mean age from the earlier year is contained in the interval, there is not sufficient evidence to conclude that the mean age had changed. d. since the mean age from the earlier year is not contained in the interval, there is sufficient evidence to conclude that the mean age had changed.

Explanation:

Step1: Recall the concept of confidence interval

A confidence interval gives a range of values within which the population mean is likely to lie. If the hypothesized value (in this case, the mean age from the earlier year, which is \(40.1\)) is within the confidence interval \((34.95,41.65)\), we fail to reject the null hypothesis (in a hypothesis - testing context related to whether the mean has changed). If it is not within the interval, we reject the null hypothesis.

Step2: Check the position of the earlier - year mean

The mean age from the earlier year \(40.1\) is contained within the confidence interval \((34.95,41.65)\). When the hypothesized value (the mean from the earlier year) is within the confidence interval, it means that the sample data does not provide strong enough evidence (at the \(95\%\) confidence level) to conclude that the population mean (the mean age of death - row inmates) has changed.

Answer:

C. Since the mean age from the earlier year is contained in the interval, there is not sufficient evidence to conclude that the mean age had changed.