Question

Height can be an advantage in many sports, but being tall is likely to provide particular advantages in basketball. The Excel file SportHeight.xls contains heights (in feet) of professional players of American football and basketball.

HtFt	HtBk
6.33	6.08
6.5	6.58
6.5	6.25
6.25	6.58
6.5	6.25
6.33	5.92
6.25	7
6.17	6.41
6.42	6.75
6.33	6.25
6.42	6
6.58	6.92
6.08	6.83
6.58	6.58
6.5	6.41
6.42	6.67
6.25	6.67
6.67	5.75
5.91	6.25
6	6.25
5.83	6.5
6	6
5.83	6.92
5.08	6.25
6.75	6.42
5.83	6.58
6.17	6.58
5.75	6.08
6	6.75
5.75	6.5
6.5	6.83
5.83	6.08
5.91	6.92
5.67	6
6	6.33
6.08	6.5
6.17	6.58
6.58	6.83
6.5	6.5
6.25	6.58
6.33
5.25
6.67
6.5
5.83

1. Is this a paired or unpaired situation?
2. Use a parametric test to determine whether basketball players are significantly taller on average than American football players. State clearly the null and alternative hypotheses and show all steps in the hypothesis test.
3. Use a nonparametric test to determine whether basketball players are significantly taller on average than American football players. State clearly the null and alternative hypotheses and show all steps in the hypothesis test.
4. Which of the two tests is most appropriate here?

Answer 1

a. It is a unpaired situation because height of football players is independent of the height of basketball players and vice versa.

b. The result obtained from SPSS is as following.

$H_0: \mu_1=\mu_2\\ vs\\ H_0: \mu_1\neq \mu_2$

as the p value is 0.000, we reject the null hypothesis.

Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Mean Std. Error Difference sig. (2-tailed)Difference Sig df Lower Upper Height Equal variances 3.684 684 411 83 .27436 07447 42248 .12624 assumed 27436 3.718 82.907 Equal variances not assumed 07380 -.42115 .12757

c. The non parametric outcome:

Nonparametric Tests [DataSetl] Hypothesis Test Summary Null Hypothesis Test Sig.Decision Independent- Mann- Test Reject the hypothesis. The distribution of Height is theSamp 001 null same across categories of Team. Whitney U Asymptotic significances are displayed. The significance level is.05.

d. The non parametric test is more accurate as no parametric information is not provided.