Question

Hypothesis Testing T-TEST for a mean

I CLAIM HEIGHT DOES NOT APPEAR TO HAVE AN EFFECT ON ACCURACY OF FREE THROWS SHOTS BY BASKET BALL PLAYERS. IF ANYTHING SHORTER PLAYERS TEND TO BE SLIGHTLY MORE ACCURATE. WITH THE DATA BELOW

A.FIND THE CRITICAL VALUE

B. COMPUTE THE SAMPLE TEST VALUE

C.MAKE THE DECISION TO REJECT OR NOT TO REJECT THE NULL HYPOTHESIS

D. SUMMARIZE THE RESULTS

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

WRITE CLEAR SO I UNDERSTAND PLEASE PREFERRED TYPED

Answer 1

To answer above question we use  t-test for Two Means are Equal Methodology

NH: HEIGHT DOES NOT APPEAR TO HAVE AN EFFECT ON ACCURACY OF FREE THROWS SHOTS BY BASKET BALL PLAYERS (H0: u1 = u2)

AH: There is a effect of Height on Accuracy of free throws shots by basket ball players(H_A: u₁ ≠ u₂)

1.) Critical Value: Many statistical hypothesis tests return a p-value that is used to interpret the outcome of the test. Some tests do not return a p-value, requiring an alternative method for interpreting the calculated test statistic directly. A statistic calculated by a statistical hypothesis test can be interpreted using critical values from the distribution of the test statistic.

We can summarize this interpretation as follows:

• Test Statistic <= Critical Value: Fail to reject the null hypothesis of the statistical test.
• Test Statistic > Critical Value: Reject the null hypothesis of the statistical test.

For above problem critical value calculated as : this data fallows a sampling distribution called t-distribution with (n₁ + n₂ -2 ) degrees of freedom. So n1=17 & n2=17 then degrees of freedom will be 17+17-2=32. We have to use t-table(https://www2.palomar.edu/users/rmorrissette/Lectures/Stats/ttests/ttests.htm) at 32 df with 5% of alpha (Level of significance) critical value with two tailed is 2.042 (use the closest value to 98 without going over)

2.) Test Statistic Value(T): we use the formula

Using above formula t-test statistic value is -27.479.

3.) DECISION : Computed value > Critical value and below table gives probability of rejection Null hypothesis :

P(T<=t) one-tail	3.97131E-24
t Critical one-tail	1.693888748
P(T<=t) two-tail	7.94261E-24
t Critical two-tail	2.036933343

P values are < Alpha(5%) so reject Null hypothesis

4.:Summary: As Test statistic & Probability values indicates, we are rejecting Null Hypothesis and going for alternative hypothesis. So values indicates towards the negative side of the curve which means if the shorter players tend to be more accurate in throw.