Question

A local manufacturer of tables wants to confirm that the mean height of adult males is 70". In a random sample of 121 men, the mean height is 71" with a standard deviation of 2". At the .05 level of significance, can we conclude that there has been a change in the mean height?

A) State the null and alternate hypothesis:

B) Name the Test

C) Determine the P-value: ______________ write as a decimal.

D) Determine whether to Reject H0 or Fail to Reject H0 , and TELL WHY by relating P-value to α:

E) Interpret the result in a complete sentence with wording related to the problem

Answer 1

This is a one-sample t-test as the population standard deviation is unknown.

Null Hypothesis: μ = 70

Alternate Hypothesis: μ =/ 71

The test statistic:

t = (x - μ)/(s/√n)

s = standard deviation = 2
x = 71
n = 121

t = (71 - 70)/(2/11)

t = 11/2 = 5.5
Therefore, test statistic t = 5.5

c) The p-value at df = 121 - 1 = 120 is: <0.001

d) As the p-value<0.05, we will reject the null hypothesis.

e) We conclude that there has been a change in the mean height of adult males.