Question

AM -vs- PM Height: 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 30 adults, the mean difference between morning height and evening height was 5.7 millimeters (mm) with a standard deviation of 1.5 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 0.05 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 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.


(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)

The null and alternate hypothesis are:

H0:

Ha:

So, this is a right-tailed test.

Hence 1st option is the correct option.

b)

The test statistic is given by:

c)

Since this is a right-tailed test, so the p-value is given by:

d)

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Thus ,we reject H0.

Hence 1st option is the correct option.

e)

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

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

Hence 1st option is the correct option.