Question

Does shorter player shoot more free throws?

Calculate the 95% Confidence Interval(Interval Estimation) for the data below.?

    Player                                       Height                                Free Throw %

Giannis Antetokounmpo	6’11	72.9
Thanasis Antetokounmpo	6’6	50.0
Dragan Bender	7’0	65.0
Eric Bledsoe	6’1	79.4
Sterling Brown	6’5	74.7
Pat Connaughton	6’5	79.1
Donte DiVencenzo	6’4	76.3
George Hill	6’3	80.2
Ersan llyasova	6’9	77.4
Kyle Korver	6’7	87.7
Brook Lopez	7’0	79.3
Robert Lopez	7’0	75.5
Frank Mason III	5’11	77.0
Wesley Matthews	6’4	82.6
Kris Middleton	6’7	87.0
Cameron Reynolds	6’7	88.9
D.J. Wlison	6’10	56.0

Answer 1

In this problem first I have converted the given height in inches as follows-

we know , 1 foot =12 inches . Thus, 6'11=(6*12)+11=72+11=83 inch. Similarly for others.Now to obtain X bar , Ybar and pooled variance I had used EXCEL as follows=

U Here, we have to test whether shorter player shoot more free throws? se we have one sided alternative H, le call Where l - Average Height & i- Average free throw Thus, confidence interval is also one-sided given by - 2 (x-7)+ tn tn 2,8 * 12 X = 7 = s = sample mean of height - sample mean of free pooled variance a

Data - Data analysis - 2 sample t test. It gives output as follws:

From above output confidence interval as follows-

t-Test Two-Sample Assuming Equal Variances height(in inches) free throw 83 72.9 - 78 50 84 65 79.4 77 74.7 79.1 76.3 80.2 81 77.4 73 77 COM 7 76 75 height free throw Mean 78.70588 75.82353 Variance 15.34559 108.0394 Observati 17 17 Pooled Va 61.6925 Hypothesi 0 df t Stat 1.069893 P(T<=t) on 0.146336 t Critical o 1.693889 P(T<=t) tw 0.292671 t Critical t 2.036933 9 32 10 79 87.7 11 84 79.3 84 75.5 77 71 76 82.6 79 14 15 16 17 87 79 88.9 82 56

s. 95% confidence interval is, I-00, (78.70588 – 75.82353) + t21717-297 * 7.8544 C os , 2.882 35 + 1.69389 7. 85444 0.3429) (-as , 7.444) As o is included in above that. There is not enough shorther player shoot more interval, we conclude evidence to conclude free throws.