Question

It is widely accepted that people are a little taller in the morning than at night. Here we perform a test on how big the difference is. In a sample of 32 adults, the mean difference between morning height and evening height was 5.5 millimeters (mm) with a standard deviation of 1.8 mm. Test the claim that, on average, people are more than 5 mm taller in the morning than at night. Test this claim at the 0.01 significance level.

(a) The claim is that the mean difference is more than 5 mm (μ_d > 5). What type of test is this?

This is a left-tailed test.This is a two-tailed test.     This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t

_d

=  

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(e) Choose the appropriate concluding statement.

The data supports the claim that, on average, people are more than 5 mm taller in the morning than at night.There is not enough data to support the claim that, on average, people are more than 5 mm taller in the morning than at night.     We reject the claim that, on average, people are more than 5 mm taller in the morning than at night.We have proven that, on average, people are more than 5 mm taller in the morning than at night.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: : Mean of population Ho : = 5 HA: >5 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat 5.5 0.31819805 31 1.5713484 P-value 0.0631

Hence,

a) This is a right tailed test.

b) Test statistic = 1.57

c) P - value = 0.0631

d) Fail to reject Ho

e) There is not enough data to support the claim that, on average, people are more than 5 mm taller in the morning than at night.