Acording to a survey in a country. 35% of adults do not have any credit cards. S

Question

Acording to a survey in a country. 35% of adults do not have any credit cards. Supos e a sim le random sample of 600 adults is obtained. a) Describe the sampling distribution of p. the sample proportion of adults who do not have a credit card. Choose the phrase that best descibes the shape of the sampling distribution of p below. OA. Not normal because ns 0.05N and np(1-p)210 O B. Not normal because ns 0.05N and np(1-p)10 c. Approximately normal because n s 0.05N and np(1-p-10 O D. Approximately normal because ns 0.05N and np(1-p)2 10 Determine the mean of the sampling distribution of p. = (Round to two decmal places as needed.) Determine the standard deviation of the sampling distribution of p ^ = (Round to three decimal places as needed.) Click to select your answer(s).

Explanation / Answer

Solution:- p = 0.35 , n = 600
a) np = 600(.35) = 210 > 10 Yep!
n(1-p) = 600(1-.35) = 390 > 10 Yep!

=> option D. Approximately normal because n <= 0.05N and np(1-p) >= 10

mean = 0.35 or => np = 0.35*600 = 210
sd = sqrt {[(p)(1-p)]/(600)} = sqrt(0.35*0.75/600) = 0.0209

b) =>P(Z < (phat - p)/sqrt(p * (1-p)/n)
P(Z < (0.33 - 0.35)/0.0209)
P(Z < -0.9569)
= 0.1685

C) p-hat = 234/600 = 0.39

p(Z > (0.39 - 0.35)/0.0209)
= P ( Z>1.9138 )
= 1P ( Z<1.9138 )
= 10.9719
= 0.0281

=> option C) The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%.

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