Question

A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course’s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is know that the population standard deviation is 8. The instructor has recommended that the students devote 36 hours to the course for the semester. Test to determine at the 1% significance level whether there is evidence that the average student spent less than the recommended amount of time. 31 40 26 30 36 38 29 40 38 30 35 38

Answer 1

Given:

n = 12, = 8, = 36 hours, = 1% = 0.01

Here, Population standard deviation () is given, So we can use Z test.

Calculation:

Sample Mean:

Hypothesis:

Ho: = 36 hours

Ha: < 36 hours

Test statistic:

Critical value:

Z =Z0.01 = - 2.33             ..................Using standard Normal table

Decision Rule:

Z < Z , Then Reject Ho at % level of significance.

Conclusion:

Z > Z, i.e. -0.76 > -2.33, That is Fail to Reject Ho at 1% level of significance.

Therefore, there is Not sufficient evidence that the average student spent less than the recommended amount of time.