Question

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.7 years with a standard deviation of 6.8 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.

1)Calculate the following.

(i) Enter your answer to one decimal place.
x =
(ii) Enter your answer to one decimal place.
s =
(iii) Enter your answer as a whole number.
n =

2)State the distribution to use for the hypothesis test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

3) Find the p-value. (Round your answer to four decimal places.)

Answer 1

Solution:

1)

(i)

= 17.7

(ii)

s = 6.8

(iii)

n = 75

2)

Since the population SD is unknown , we use t distribution.

df = n - 1 = 75 - 1 = 74

Suppose , significance level = 0.05

/2 = 0.025

t_df= t_74,0.025 = 1.992

3)

Hypothetical value : = 15

The test statistics t is given by ..

t =  

= (17.7 - 15)/(6.8/75)

= 3.439

Using t = 3.439 , df = 74 , TWO tailed test ,

p value = 0.0010