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 hypothesis are
Ho: p1-p2=0
Ha:p1-p2>0
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?
A) If the rate of depression in male and female
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 the 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 female
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
D) Both B and C bot not A