Answer
a. For $H_0$, $p=.5$; For $H_1$, $p>.5$
b. .01
c. Normal
d. Right-tailed
e. 1.00
f. .1587
g. 2.33
h. .01
Work Step by Step
a. The null hypothesis is the average fraction of girls, which is .5, and the alternative hypothesis is that more than 50 percent of births are girls, which is $p>.5$.
b. $\alpha $ is the significance level, which the problem states is .01.
c. We see that the sample distribution of the sample statistic is a normal distribution.
d. There are more girls in the survey, so the two-test is right tailed.
e. The problem states that the sample statistic is 1.00.
f. Using the table of z-scores, we find that:
$P=1-.8413=.1587$
g. Using the table of z-scores, we find that the critical value is 2.33.
h. Since the significance level is .01, it follows that the area of the critical region is .01.
