Question

Question Help One year, the mean age of animate on death row was 38.4 years. A sociologist wondered whether the mean age of a deathrow inmate has changed since then. She randomly selects 32 deathrow inmates and finds that their mean age is 373, with a standard deviation of 98. Construct a 95% confidence interval about the mean age. What does the interval imply? Click the icon to view the table of critical values Choose the correct hypotheses HE Type integers of decimas. Do not found.) Construct a 95% confidence interval about the mean age The lower bound is The upper bound is Round to two decimal places needed) What does the interval imply? Cho to set your answers MacBook Air P * 80 RUE D G 4B R 7 ASDFGH :

Answer 1

H0: mu = 38.4
Ha: mu not equals to 38.4

sample mean, xbar = 37.3
sample standard deviation, s = 9.8
sample size, n = 32
degrees of freedom, df = n - 1 = 31

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.04

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (37.3 - 2.04 * 9.8/sqrt(32) , 37.3 + 2.04 * 9.8/sqrt(32))
CI = (33.77 , 40.83)

lower bound = 33.77 ,
upper bound = 40.83

Interval implies : as 38.4 is included in the CI, fail to reject H0
The mean has not changed