Question

A professor in the education department believes that OU students study less hours per week when compared to the general population of university students. The general population of university students studies an average of 15 hours a week with a standard deviation of 2. The professor randomly samples 16 OU students and discovers her sample has a mean of 12. Use an alpha level of 0.05 to determine whether OU students study less hours per week when compared to the general population.

a. State the null and alternative hypotheses in words.

b. Set up the criteria for making a decision. That is, find the critical value (s).

c. Compute the appropriate test statistic. Show your work.

d. Based on your answers above, evaluate the null hypothesis.

REJECT FAIL TO REJECT (circle one)

e. State your conclusion in words.

f. Given your decision, what type of error could have been committed?

Type I error Type II error (circle one)

Answer 1

a) Hypothesis can be framed as -

Null hypothesis : The OU students study equally as the general population of University students.

The average study hours of OU students = 15

Alternative hypothesis : The OU students study less hours per week when compared to the general population.

The average study hours of OU students < 15

b) The critical value of z for one tailed test at 0.05 level of significance = -1.645

It can be obtained from the z table by finding the z corresponding to area approximately equal to 0.05 and it will be at -1.6 at probability between 0.04 and 0.05 so value will be -1.645.

If the value if test statistic is less than this critical value, we will reject the null hypothesis otherwise, we will not reject it.

c) Test statistic is given by -

where, The hypothesed value of Population mean under the null hypothesis = = 15 hours per week

Population standard deviation = = 2 hours per week.

Sample size = n = 16

Sample mean = = 12

Hence, the value of test statistic will be -

= -6

Level of significance = = 0.05

d) Since, the value of test statistic (-6) < critical value of z, we will reject the null hypothesis.

So, answer is Reject

e) Hence, we conclude that the OU students study less than the general population of University students.

f) Since, we have rejected the null hypothesis, if our decision is wrong, that is the null hypothesis is true, then , we will commit Type I errror.