Question

Does the use of sweetener xylitol reduce the incidence of ear infections? Some children are randomly allocated t xylitol treatment group and other children to the control group (who are treated with placebo). Of 285 children on xylitol, 72 got ear infection, while of 229 children on placebo, 57 got ear infection.
Suppose p1p1 and p2p2 represent population proportions with ear infections on xylitol and placebo, respectively. Again p^1p^1 and p^2p^2 represent sample proportions with ear infections on xylitol and placebo, respectively.

1. What are the appropriate hypotheses one should test?
A. H0:p^1=p^2H0:p^1=p^2 against Ha:p^1>p^2Ha:p^1>p^2 .
B. H0:p^1=p^2H0:p^1=p^2 against Ha:p^1≠p^2Ha:p^1≠p^2 .
C. H0:p1=p2H0:p1=p2 against Ha:p1<p2Ha:p1<p2 .
D. H0:p1=p2H0:p1=p2 against Ha:p1≠p2Ha:p1≠p2 .
E. H0:p1=p2H0:p1=p2 against Ha:p1>p2Ha:p1>p2 .
F. H0:p^1=p^2H0:p^1=p^2 against Ha:p^1<p^2Ha:p^1<p^2 .

2.Rejection region: We reject H0H0 at 5% level of significance if:
A. z<−1.960z<−1.960 .
B. z>1.645z>1.645 .
C. |z|>1.960|z|>1.960 .
D. z<−1.645z<−1.645 .
E. |z|>1.645|z|>1.645 .
F. None of the above

3.The value of the test-statistic is: Answer to 2 decimal places.

4. If α=0.05α=0.05 , what will be your conclusion?
A. Reject H0H0 .
B. Do not reject H0H0 .
C. There is not enough information to conclude.

5. The p-value of the test is: Answer to 4 decimal places.

6. We should reject H0 for all significance level (αα ) which are
A. larger than p-value.
B. smaller than p-value.
C. not equal to p-value.

Answer 1