Answer
a) For $H_0$, $p=0.5 $; For $H_1$, $p\gt0.5$
b) $0.01$
c) Normal
d) Right-tailed
e) $1.00$
f) $0.1587$
g) $2.33$
h) $0.01$
Work Step by Step
a) The null hypothesis is the average fraction of girls, which is $0.5$, and the alternative hypothesis is that more than 50 percent of births are girls, which is $p\gt0.5$.
b) $α$ is the significance level, which the problem says is $0.01$.
c) We can 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 says that the sample statistic is $1.00$.
f) Using the table of z-scores, we can find that:
$P=1−0.8413=0.1587$
g) Using the table of z-scores, we can find that the critical value is $2.33$.
h) The significance level is $0.01$, hence the area of the critical region is $0.01$.
