Question

AM -vs- PM Height (Raw Data, Software Required):
We want to test the claim that people are taller in the morning than in the evening. Morning height and evening height were measured for 30 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded in the table below. Use this data to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.10 significance level.

(a) In mathematical notation, the claim is which of the following? μ < 0μ > 0     μ ≠ 0μ = 0 (b) What is the test statistic? Round your answer to 2 decimal places. t x =    (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 taller in the morning than in the evening.There is not enough data to support the claim that on average people are taller in the morning than in the evening.     We reject the claim that on average people are taller in the morning than in the evening.We have proven that on average people are taller in the morning than in the evening.

DATA ( n =  30 ) AM-PM Height Difference cm     -0.15 0.35 0.68 0.17 -0.38 0.00 -0.05 0.58 -0.09 0.62 0.82 0.33 1.16 0.25 0.28 -0.30 -0.13 0.86 -0.26 0.05 0.55 -0.15 0.02 -0.24 0.17 0.17 0.68 0.42 0.23 -0.15

Answer 1

Let us denote : d = height in AM - height in PM

Let denote the average value of the difference.

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.10 level of significance if P-value < 0.10

Now,

The value of the test statistic =

P-value =

Since p-value < 0.10, so we reject H₀ at 0.10 level of significance and we can conclude that :

The data supports the claim that on average people are taller in the morning than in the evening.