Write the word or phrase that best completes each statement or answers the quest
ID: 3267204 • Letter: W
Question
Write the word or phrase that best completes each statement or answers the question. A weight- lifting coach claims that weight- lifters can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength. Assume the samples are random and dependent, and the populations are normally distributed. Use alpha = 0.05. Explain how you computed the sample means and standard deviations. Suggestion: use ExcelExplanation / Answer
Solution
Let X = strength before training with supplement and Y = strength after training with supplement.
Let D = X – Y.
Given, X and Y are normally distributed, D ~ Normal, say with mean µ and variance 2.
Claim: Supplement is effective in increasing the strength of athletes.
Hypotheses:
Null H0: µ = µ0 = 0 Vs
Alternative HA: µ > 0 [claim]
Test statistic:
t = (n)(Dbar - µ0)/SD(D), where
n = sample size (9), Dbar = sample average of D and SD(D) = sample standard deviation of D.
Excel calculation summary is given below:
i
xi
yi
di = yi - xi
1
215
225
10
2
240
245
5
3
188
188
0
4
212
210
-2
5
275
282
7
6
260
275
15
7
225
230
5
8
200
195
-5
9
185
190
5
Dbar
4.444444
s^2(D)
33.35802
SD(D)
5.775641
tcal
2.308546
Distribution, Critical Value and p-value
Under H0, t ~ tn - 1
Critical value = upper % point of tn – 1 (t8)
p-value = P(tn – 1 > tcal) = 0.025
Given = 0.05, tcrit = 1.860
[Both tcrit and p-value are obtained using Excel Functions]
Decision Criterion (Rejection Region)
Reject H0, if tcal > tcrit or p-value < .
Decision:
Since tcal > tcrit, H0 is rejected.
Since p-value < . H0 is rejected..
Conclusion:
There is sufficient evidence to support the claim that supplement is effective in increasing the strength of athletes.
DONE
i
xi
yi
di = yi - xi
1
215
225
10
2
240
245
5
3
188
188
0
4
212
210
-2
5
275
282
7
6
260
275
15
7
225
230
5
8
200
195
-5
9
185
190
5
Dbar
4.444444
s^2(D)
33.35802
SD(D)
5.775641
tcal
2.308546
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