According to the American Dental Association, 8% of adults have never had a cavity. A dental graduate student contacts an SRS of 1000 adults and calculates the proportion p-hat in this sample who have never had a cavity.
a. Identify the mean of the sampling distribution of ô.
b. Calculate and interpret the standard deviation of the sampling distribution of p.
c. Is the sampling distribution of p approximately Normal? Check that the Large Counts condition
is met
d. Find the probability that the random sample of 1000 adults will give a result within 2
percentage points of the true value. (6%-10%)
e. If we take a random sample of 1000 adults and find that 10% have never had a cavity, does
this provide convincing evidence that the American Dental Association needs to update their
statistics and there is more than 8%?