Question

Compare the height, weight (in inches), and age for Eagles versus Patriots, using t tests. Provide the conclusions based on the t tests.

Eagles

Age			Height (")
35			66
28			69
			69
23			69
23			69
29			69
23			70
24			70
31			70
28			70
24			70
24			71
24			71
26			71
31			71
23			71
26			71
25			72
25			72
31			72
29			72
33			72
30			72
22			72
28			72
23			72
24			72
29			72
23			72
24			72
26			73
32			73
26			73
24			73
23			73
29			74
24			74
23			74
30			74
24			74
26			74
38			74
26			74
24			74
25			74
27			74
25			74
26			75
22			75
26			75
30			75
25			75
28			75
30			75
33			75
28			75
25			75
29			75
25			76
33			76
27			76
25			76
36			76
24			76
24			76
26			76
31			77
29			77
27			77
			77
25			77
27			77
33			78
29			78
28			78
24			78
25			78

Pats

Age			Height (")
28			75
28			74
32			71
26			75
28			72
31			78
28			71
41			76
33			78
30			75
24			74
28			70
24			76
28			71
30			78
26			75
31			71
25			70
24			77
24			75
30			75
25			70
29			72
32			70
25			76
29			74
26			78
26			75
25			74
24			79
27			71
28			73
34			73
26			74
26			76
29			78
28			76
27			73
34			74
40			72
28			75
29			73
24			76
24			76
32			74
31			75
24			78
24			70
24			75
25			70
25			76
24			77
25			74
24			76
26			74
24			75
28			68
24			72
25			73
25			69
31			70
26			68
25			71
24			77
24			72
25			73
33			72
30			80
25			77
24			74
26			74
24			75
27			75
27			78
26			70
23			70
24			77

Answer 1

Here we want to test that there is significant differecne between heights of Eagles and Patriots at 5% level of significance.

Let's use minitab:

Choose Stat > Basic Statistics > Paired t

Choose Samples in columns

Sample in columns: Choose if you have entered raw data in two columns.

First sample: Enter the column containing the first sample

Second sample: Enter the column containing the second sample

   versus   

where is the population mean of the differences.

So we get following output

MTB > Paired 'Height_Eagles' 'Height_Pats'.

Paired T-Test and CI: Height_Eagles, Height_Pats

Paired T for Height_Eagles - Height_Pats

              N    Mean StDev   SE Mean
Height_Eagles    77 73.519 2.664    0.304
Height_Pats       77 73.948 2.790    0.318
Difference    77 -0.429    3.995    0.455

95% CI for mean difference: (-1.335, 0.478)

T-Test of mean difference = 0 (vs not = 0): T-Value = -0.94 P-Value = 0.349

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.349 > 0.05 so we used 2nd rule.

That is we failed reject null hypothesis

Conclusion:

At 5% level of significance there are sufficient evidence to say that the sample data indicates that there is no significant differecne between heights of Eagles and Patriots.