Question

1. A researcher wants to support the claim that students spend less than 7 hours per week doing homework. The sample size for the test is 64 students. The drawing shown diagrams a hypothesis test for population mean under the Null Hypothesis (top drawing) and under the Alternative Hypothesis (bottom drawing).
   
   

   1. State the Null and Alternative Hypotheses.

Ha :

Ho :

2. What is the design probability associated with Type I error?

3. What is the design probability associated with Type II error?

4. What is the power of the test shown in this graph?

5. If the p-value of the test came out to be .08, what would the decision be? Also, write the conclusion in the context of the problem

6. What is the value of the mean under the Alternative Hypothesis?

7. What is the effect size of this test? Explain what it means

.

8. If the sample size was changed to 100, would the shaded area on the bottom graph increase, decrease or stay the same?

Answer 1

g) From the below diagram, the mean under the alternative hypothesis is as

= 2

from part b) let's find sigma as

For area = 0.07

z = "=NORMSINV(0.07)" = -1.48

= 3 * 8 / 1.48 = 16.22

effect size = 5/16.22 = 0.308

which is greater than 0.2 and less than 0.5

So effect size is medium.

So rejecting null hypotheses is only marginally if the mean under alternative is 2.