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 39.5​, with a standard deviation of 8.6. 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​: ▼ sigma x over bar mu p ▼ less than not equals greater than equals nothing

Upper H 1​: ▼ sigma mu p x over bar ▼ greater than not equals less than equals nothing

​(Type integers or decimals. Do not​ round.)

Construct a​ 95% confidence interval about the mean age. The lower bound is nothing. The upper bound is nothing. ​

(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 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 not 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 contained in the​ interval, there is not sufficient evidence to conclude that the mean age had changed.

Answer 1

x̅ =    39.5
s =    8.6
n =    32
  
Null and Alternative hypothesis:  
Ho : µ = 40.5
H1 : µ ≠ 40.5

95% Confidence interval :  

At α = 0.05 and df = n-1 = 31, two tailed critical value, t-crit = T.INV.2T(0.05, 31) = 2.040

Lower Bound = x̅ - t-crit*s/√n = 39.5 - 2.04 * 8.6/√32 = 36.40

Upper Bound = x̅ + t-crit*s/√n = 39.5 + 2.04 * 8.6/√32 = 42.60

36.40 < µ < 42.60

Answer : D. 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.