You are testing the claim that a male's self-reported height is different from his actual height. In the table below are the differences in the self-reported and clinically measured heights for 30 males. (abstract). Test the claim using a 5% level of significance. For the context of this problem, $\displaystyle {x}_{{d}}={x}_{\text{self}}-{x}_{\text{clinical}}$, we find the differences, then test the mean difference. Assume that heights are normally distributed.

You may use StatKey Hypothesis Test for a Single Mean

Height Difference (x_d)
4.09
4.33
-9.26
0.71
6.75
-1.97
1.77
5.7
5.58
5.56
5.25
2.84
1.17
-4.95
6.52
2.18
1.12
-0.01
1.53
2.58
3.89
4.24
-4.46
-2.82
1.26
2.03
-3.04
2.67
-1.43
0.32

What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem.

H₀: Select an answer x̅₁ x̅₂ μ₁ σ² μ_d p s² μ₂  ? ≠ > ≤ < ≥ = Select an answer μ₁ x̅₂ σ² p μ₂ s² x̅₁ 0

H_a: Select an answer s² μ₂ p μ_d μ₁ σ² x̅₂ x̅₁ ? < ≠ > ≥ = ≤ Select an answer μ₁ s² x̅₂ p x̅₁ 0 σ² μ₂

Based on the hypotheses, find the following:

Test Statistic = (Hint: $\displaystyle \mu_{{d}}$)

p-value =

The correct decision is to Select an answer accept the null hypothesis reject the claim accept the alternative hypothesis fail to reject the null hypothesis reject the null hypothesis .

The correct summary would be: Select an answer There is enough evidence to reject the claim There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to support the claim that the mean difference in height of a male, between what is self-reported and clinically measured, is not zero.