(c) Suppose that an average increase in score of 5 points (F5) and standard devi
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Question
(c) Suppose that an average increase in score of 5 points (F5) and standard deviation of s = 25 points were found in each of the following scenarios. Further, assume difference in score is normally distributed. For each case, compute the test statistic and, given the p value, make a decision about the null hypothesis using an 0.05 level of significance. Round t-statistics to two decimals. i. Scenario 1: a sample of size n 10 A, t= B. The p-value corresponding to the correct test statistic is 0.271. Decision: and df = . Reject the null hypothesis. ·Fail to reject the null hypothesis. ii. Scenario 2: a sample of size n = 80 A. t= B. The p-value corresponding to the correct test statistic is 0.039. Decision: and df= - Reject the null hypothesis because the p-value . Reject the nu hypothesis because the p-value >a . Fail to reject the null hypothesis because the p-value a O. Scenario 3: a sample of size n 800 A. t= and df = decision and indicate the type of error possible.Explanation / Answer
i) for std error of mean =std deviatrion/(n)1/2 =25/(10)1/2 =7.906
test statistic t=xbar/std error =5/7.906 =0.63
df =n-1=9
fail to reject the null hypothesis.
(ii)
std error of mean =std deviatrion/(n)1/2 =25/(80)1/2 =2.795
test statistic t=xbar/std error =5/2.795 =1.79
df =n-1=79
reject the null hypothesis because the p value <=alpha
*iii)
std error of mean =std deviatrion/(n)1/2 =25/(800)1/2 =0.884
test statistic t=xbar/std error =5/0.884 =5.66
df =n-1=799
reject the null hypothesis because the p value <=alpha
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