Question

AM -vs- PM Height: 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 32 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded. The mean difference was 0.21 cm with a standard deviation of 0.40 cm. Use this information to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.05 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 H0 fail 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.

Answer 1

a)

Claim: People are taller in the morning than in the evening.

The null and alternative hypothesis is

HO : μα = 0

Hi: pd > 0

Level of significance = 0.05

Sample size = n = 32

Sample mean of difference = $\bar{d}$ = 0.21

Sample standard deviation of difference = $s_{d}$ = 0.40

b)

Test statistic is

t = Sd/ n

t= 0.21 = 0.40/32 0.21 0.0707 = 2.97

c)

Degrees of freedom = n - 1 = 32 - 1 = 31

P-value = P(T > 2.97) = 0.0029

d)

P-value < 0.05 we reject null hypothesis.

e)

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