Question

A randomly selected sample of college basketball players has the following heights in inches. 63, 62, 71, 63, 63, 63, 69, 61, 68, 64, 62, 62, 65, 69, 69, 71, 66, 62, 63, 64, 66, 61, 63, 67, 65, 64, 63, 61, 68, 68, 67, 62. Compute a 93% confidence interval for the population mean height of college basketball players based on this sample and fill in the blanks appropriately.

Answer 1

For the confidence interval, we first obtain the sample mean and sample standard deviation here as:

X	X - Mean(X)	(X - Mean(X))^2
63	-1.84375	3.399414063
62	-2.84375	8.086914063
71	6.15625	37.89941406
63	-1.84375	3.399414063
63	-1.84375	3.399414063
63	-1.84375	3.399414063
69	4.15625	17.27441406
61	-3.84375	14.77441406
68	3.15625	9.961914063
64	-0.84375	0.711914063
62	-2.84375	8.086914063
62	-2.84375	8.086914063
65	0.15625	0.024414063
69	4.15625	17.27441406
69	4.15625	17.27441406
71	6.15625	37.89941406
66	1.15625	1.336914063
62	-2.84375	8.086914063
63	-1.84375	3.399414063
64	-0.84375	0.711914063
66	1.15625	1.336914063
61	-3.84375	14.77441406
63	-1.84375	3.399414063
67	2.15625	4.649414063
65	0.15625	0.024414063
64	-0.84375	0.711914063
63	-1.84375	3.399414063
61	-3.84375	14.77441406
68	3.15625	9.961914063
68	3.15625	9.961914063
67	2.15625	4.649414063
62	-2.84375	8.086914063
2075		280.21875

The sample mean and sample standard deviation here are computed as:

For n - 1 = 31 degrees of freedom, we have from the t distribution tables here:

P( t₃₁ < 1.877) = 0.965  

Therefore, due to symmetry, we have here:
P( -1.877 < t₃₁ < 1.877) = 0.93

Now the confidence interval here is obtained as:

This is the required 93% confidence interval for the population mean height here.