Previous studies suggest that female teens are more likely to be
depressed than male teens. Define the depression rates for the
female and male teens as p1 and p2, respectively. If we claim that
the depression rate is higher for female teens (p1 > p2), the
null and alternative hypotheses are:
We test the hypotheses at a 5% significance level. Suppose we
randomly select 100 female teens and determine that 14 are
clinically depressed. Among 200 randomly selected male teens, 16
are clinically depressed.
Since the normal model is a good fit, we can use the standard
normal curve to find the P-value. The P-value is about 0.051.
Which is the correct interpretation of the P-value?
Group of answer choices
a. If the rate of depression in male and females teens is the
same, the probability that in the random samples of 100 females and
200 males, female depression rates will differ from male depression
rates by more than 6% is 0.051.
b. There is a 5.1% chance that in population of teens the
proportion of female teens who are depressed is equal to the
proportion of male teens who are depressed.
c. If the rate of depression in male and females teens is the
same, the probability that in the random samples of 100 females and
200 males, female depression rates will differ from male depression
rates by less than 6% is 0.051.
Both b and c but not a