Question

6. 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 34 adults, the mean difference between morning height and evening height was 5.6 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 0.10 significance level. (a) The claim is that the mean difference is more than 5 mm (μd > 5). What type of test is this? This is a right-tailed test. This is a left-tailed test. This is a two-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 H0 fail 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

a)

This is a right-tailed test.

b)

test statistic t =1.94

c) p value =0.0303 (please try 0.0305 if this comes wrong due to rounding error)

d)

since p value <0.10

reject H0

e)

The data supports the claim that, on average, people are more than 5 mm taller in the morning than at night.