Question

About 78% of the US, population claims that they visit the dentist at least once a year. simple random sample of 200 people is selected for a health study and the sample proportion of those who visited the dentist at least once during the year is computed. Which one of the following gives, respectively, the mean and standard deviation of the sampling distribution oft 27. the sample proportion who claim they visit the dentist at least once a year?
A)156, 12.49
B) 156, 5.86
C) 0.78, 0.012
D) 0.78, 0.029
E) You cannot determine the standard deviation from the given information.

Answer 1

Answer:

D) 0.78, 0.029

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

About 78% of the US, population claims that they visit the dentist at least once a year.

This means that $p = 0.78$

Random sample of 200 people:

This means that $n = 200$

Mean and standard deviation of the sampling distribution:

By the Central Limit Theorem

Mean $\mu = 0.78$

Standard deviation $s = \sqrt{\frac{0.78*0.22}{200}} = 0.029$

So the correct answer is given by option D.