The true average of the amount of time spent by students to do their homework in

Question

The true average of the amount of time spent by students to do their homework in minutes is supposed to be 75 volts. A professor was interested in conducting a study to check whether the students are taking enough time to make their homework. He selects a sample of 100 such students and uses the resulting recorded amount of time as a basis to perform a test. If the standard deviation is sigma = 25. Is there a compelling evidence that the true mean differ from 76 at the level of significance 0.05? Answer the question using two different ways and provide comments on the results: a) Using the critical region: b) Using the P-value:

Explanation / Answer

NULL hypothesis H0: =75 verssu alternative Ha: 75

Test statistic Z=(xbar-0)/(/sqrt(n)) =(76-75)/(25/sqrt(100))=0.4

Part-a At 5% level critical z=±1.96

As calculated Z<1.96, we do not reject null and conclude that the true mean does not differ from 76

Part-b-p-value=2*P(Z<-0.4)=0.6892

As p-value>0.05, we do not reject null and conclude that the true mean does not differ from 76

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