Question

Last year it was found that on average it took students 20 minutes to fill out the forms required for graduation. This year the department has changed the form and asked graduating student to report how much time it took them to complete the forms. Of the students 22 replied with their time, the average time that they reported was 18.5 minutes, and the sample standard deviation was 5.2. Can we conclude that the new forms take less time to complete than the older forms? Use a 0.1 significance level (i.e., p-value). (Assume that the reported times follow a Gaussian distribution).

Answer 1

H0: = 20

Ha: < 20

Test statistics

t = ( - ) / (S / sqrt(n) )

= ( 18.5 - 20) / ( 5.2 / sqrt(22) )

= -1.35

From T table,

With test statistics t = 1.35 and df of 21,

p-value = 0.0957

Since p-value < 0.10 significance level, Reject H0.

We conclude at 0.10 significance level that we have sufficient evidence to support the claim that

the new forms take less time to complete than the older forms