Question

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 0.01 significance level.

(a) In mathematical notation, the claim is which of the following? μ = 0 μ ≠ 0   μ > 0 μ < 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
-0.13
0.26
0.65
0.21
-0.40
-0.01
-0.06
0.60
-0.15
0.60
0.78
0.32
1.18
0.15
0.27
-0.26
-0.06
0.95
-0.26
0.07
0.59
-0.09
-0.01
-0.24
0.25
0.19
0.74
0.43
0.20
-0.11

Answer 1

First we need to find the mean and SD of differences. Following table shows the calculations:

	d	(d-mean)^2
	-0.13	0.123904
	0.26	0.001444
	0.65	0.183184
	0.21	0.000144
	-0.4	0.386884
	-0.01	0.053824
	-0.06	0.079524
	0.6	0.142884
	-0.15	0.138384
	0.6	0.142884
	0.78	0.311364
	0.32	0.009604
	1.18	0.917764
	0.15	0.005184
	0.27	0.002304
	-0.26	0.232324
	-0.06	0.079524
	0.95	0.529984
	-0.26	0.232324
	0.07	0.023104
	0.59	0.135424
	-0.09	0.097344
	-0.01	0.053824
	-0.24	0.213444
	0.25	0.000784
	0.19	0.001024
	0.74	0.268324
	0.43	0.043264
	0.2	0.000484
	-0.11	0.110224
Total	6.66	4.52068

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(e)

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