Question

1. The time it takes to do the in class problem sets averages 40 minutes. To test the hypothesis that the problem sets for hypothesis testing will be completed faster a sample of 100 students showed the average time to complete the problem sets was 32 minutes with a standard deviation of 9 minutes.

a) At the .05 level do the hypothesis tests get done faster than normal? (note: p = 0)

b) Interpret the p-value

c) The 95% confidence interval readout is “33.49 or more.” Interpret this in context of the problem

d) If I take another sample of 100 students to do a hypothesis testing problem set would a mean of 38 minutes be something I would expect? Explain

Answer 1

Let us assume that the time it takes to do the class problem follows a Normal distribution and the samples are independent. For the sample of size 100, the mean is 32 minutes with standard deviation of 9 minutes.

We want to assess,"To test the hypothesis that the problem sets for hypothesis testing will be completed faster ".  

Null Hypothesis: The average time taken to solve the in class problem=40 minutes.

Alternative Hypothesis: The average time taken to solve the problem is faster ie <40 minutes.

Test Statistic: Calculate follows a t-distribution with 100-1=99 df and at 5% level of significance.

  

  

Tabulated value for t is -1.6604. Since the Calculated value is greater than tabulated value, we reject the null hypothesis. Ie the test gets faster than the normal.  

b). Here, we get the p-value from the EXCEL function T.DIST(-8.8889,99,true) , we get the p-value as 1.4447E-14 which is almost closer to 0. Hence the p-value<0.05(our alpha level =0.05), we reject the null hypothesis.

c). The 95% confidence interval is obtained by   

  

   . We can see that the upper limit of the confidence interval is 33.764. The statement that the 95% confidence readout is 33.49 or more is not correct since 33.49 minutes is almost closer to the upper limit. The correct statement could have been 95% confidence readout is 30.24 or more and less than 33.764.

d). If we take another 100 samples, by the above confidence interval, I am expected to get a mean within 95% of the times. Hence, the statement is not true.