Question

a) A physical education director claims by taking a special vitamin, a weight lifter can

increase his strength. Eight athletes are selected and given a test of strength, using the standard bench press. After two weeks of regular training, supplemented with the vitamin, they are tested again. Test the vitamin regimen is effective in increasing strength at the .05 level of significance. Each value in the data that follow represents the maximum number of pounds the athlete can bench press. Assume both populations normal.

athlete 1 2 3 4 5 6 7 8Before 210 230 182 205 262 253 219 216

after 219 236 179 204 270 250 222 216

claim .................................................... null hypothesis........................................ alternative hypothesis................................ Calculator Screen Name........................... test statistic .............................. pvalue/alpha comparison............................ decision ............................... Conclusion ...............................

b) Construct a 95% confidence interval for, ?d , the mean difference of the before minus the after times. Interpret the interval in a complete sentence.

Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________

Answer 1

Before	After	Difference
210	219	-9
230	236	-6
182	179	3
205	204	1
262	270	-8
253	250	3
219	222	-3
216	216	0
	Total	-19

Claim: The vitamin regimen is effective in increasing strength.

The null and alternative hypothesis is

By using TI-84 we can solve this question.

First, enter the differenced value in L1

Click on STAT --------> Edit ---------> Enter differenced value in to L1

Then click on STAT -----------> TESTS ---------> T-Test --------> Data --------->Enter values -------->

: 0

List: L1

Freq: 1

Calculate

We get

Test statistic = t = - 1.40

P-value = 0.8948

P-value > 0.05 we fail to reject null hypothesis.

Conclusion:

The vitamin regimen is not effective in increasing strength.

b) Confidence interval Name: - T interval

We have to find 95% confidence interval.

TI-84 path is

Click on STAT ------->TESTS ---------> TInterval ----------->Data ----------->Enter value -------->

List: L1

Freq: 1

C-Level: 0.95

Calculate

We get confidence interval ( - 7.452 , 2.0231)

The vitamin regimen is not effective in increasing strength.