Question

Sixty percent of the people in a state plan to take a vacation this summer. If 800 people in this state are sampled, find:

a. the mean of the sampling distribution of p-hat.

b. the standard deviation of the sampling distribution of p-hat.

c. the probability that more than 65% of those sampled plan to take a vacation this summer.

d. If n is decreased from 1000, will the probability in the previoius question get bigger or smaller? Explain why.

e. If 20 people are randomly sampled, what is the probability that exactly 12 of them plan to take a vacation this summer?

Answer 1

a.

mean of the sampling distribution of p-hat = 0.6

b.

standard deviation of the sampling distribution of p-hat, SE =

= 0.01732051

c.

Probability that more than 65% = P(p-hat > 0.65)

= P[z > (0.65 - 0.6)/0.01732051]

= P[z > 2.89]

= 0.0019

d.

If sample is decreased , the standard error will increase and the test statistic will decrease. So, the probability will increase as the tail will become wider.

e.

Using Binomial distribution,

= 0.1797058