Question

One​ year, the mean age of an inmate on death row was 40.5 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 39.9​, with a standard deviation of 8.9. Construct a​ 95% confidence interval about the mean age. What does the interval​ imply?

LOADING... Click the icon to view the table of critical​ t-values.

Choose the correct hypotheses. Upper H 0​: ▼ ▼ nothing Upper H 1​: ▼ sigma mu x overbar p ▼ less than greater than equals not equals nothing ​(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 ? years and ?g years. ​(Round to two decimal places as​ needed.)

What does the interval​ imply? A. 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. B. 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. 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.

Answer 1

given data are:-

sample mean () = 39.9

sample sd (s) = 8.9

sample size (n) = 32

hypothesis:-

df = (n-1) = (32-1) = 31

t critical value for df = 31, alpha = 0.05, both tailed test be :-

[ using t distribution table ]

the 95% confidence interval about the mean age is:-

interpretation:-

With​ 95% confidence, the mean age of a death row inmate is between 36.69 years and 43.11 years.

the interval​ implies that :-

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 (C).

[ the hypothesized mean 40.5 is contained in the interval..so, we fail to reject the null hypothesis .]

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