A professor is getting evaluated for his ability to teach statistics. On a test

Question

A professor is getting evaluated for his ability to teach statistics. On a test of stats knowledge, the 49 students in his class get an average score of 71. The professor decides to put his stats knowledge to use to answer the following research question: is the average in his class different from the average score of other classes? He learns that the average grade in the other classes (the population) was a 75 with a standard deviation of 28. If alpha = 0.05, use hypothesis testing to determine if his class scored differently from the other classes. When you have made a decision about the research question, determine effect size of the difference between means.

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =4

hence from above test stat z=(X-mean)/std error =(71-75)/4 =-1

for 0.05 level critical value of z are z>1.96 and z<-1.96

as our z stat does not fall into rejection region we can not reject null hypothesis

hence we do not have sufficient evidence that class scored differently from the other classes

effect size =(mean1-mean2)/std deviation =(75-71)/28 =0.1429

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