Answer:
The z-test statistic for this hypothesis test is
Explanation:
Proportion in 2000:
10 of the 50 men were obese, so:
Test if it has increased:
At the null hypothesis, we test if the prevalence of obesity has not increased, that is, the proportion is of 0.2 or less, so:
At the alternative hypothesis, we test if this prevalence has increased, that is, the proportion is above 0.2. So
The test statistic is:
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.2 is tested at the null hypothesis:
This means that
30 out of the 75 men from 2010 were assigned as obese.
This means that
Value of the z-test statistic:
The z-test statistic for this hypothesis test is