Athletes. Developers of performance diets advertise that following their exercis
ID: 3355788 • Letter: A
Question
Athletes. Developers of performance diets advertise that following their exercise regime and nutritional plans will result in significant muscle gain. An Iowa State student developed a performance diet and conducted a study to show the effectiveness of her diet. The ISU student hopes to show that following her diet, athletes will gain muscle, and hopes that this will lead to better athletic performance on the field. Suppose she has a random sample of 30 athletes that agree to follow the performance diet and finds that the average muscle gain was 2.5 pounds with a standard deviation of s = 5.
(a) Identify µ in this scenario. (Choose One)
• Average muscle mass of all people in the sample. • True average muscle mass of all people in the population. • True average muscle mass gained by all people in the population. • Average muscle mass gained of all people in the sample.
(b) Conduct a hypothesis test of the above situation, using a significance level of =0.05.
i. Identify the hypotheses H0 and Ha.
ii. Find the test statistic (Round your answer to 2 decimal places).
iii. Using the following table, select the appropriate p-value. P(T < t) 0.995 ||| P(T > t) ||| 0.005 P(T > |t|) 0.010
iv. Provide an interpretation of the p-value you chose from the above table within the context of the problem.
v. Make a decision about H0. Use a significance level of = 0.05.
• Reject the null hypothesis because the p-value . • Reject the null hypothesis because the p-value > . • Fail to reject the null hypothesis because the p-value . • Fail to reject the null hypothesis because the p-value > .
vi. Based on your decision, write a conclusion in the context of the problem.
vii. Explain what a Type I error is in the context of this problem.
Explanation / Answer
a)µ =True average muscle mass gained by all people in the population
b) (i) Ho:µ =0
Ha:µ >0
(ii) here std error =std deviation/(n)1/2 =5/(30)1/2 =0.9129
tehrefore test statistic t=(X-mean)/std error =(2.5-0)/0.9129=2.74
(iii)from above p value =P(T > t) ||| 0.005
(iv)abvoe p value gives probability to find test statisitc as far away as we find in our test if null hypothesis is correct.
v)as p value is less then 0.05 ; we reject null hypothesis.
Reject the null hypothesis because the p-value
vi) we have sufficient evidence to conclude that that following their exercise regime and nutritional plans will result in significant muscle gain.
(vii) Type I error here is rejecting that following their exercise regime and nutritional plans will not result in significant muscle gain while in actual it does not have effect on muscle gain
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