According to a survey in a country, 17% of adults do not have any credit cards.

Question

According to a survey in a country, 17% of adults do not have any credit cards. Suppose a simple random sample of 800 adults is obtained. (a) Describe the sampling distribution of Modifying Above p with carrot, the sample proportion of adults who do not have a credit card. Choose the phrase that best describes the shape of the sampling distribution of Modifying Above p with carrot below. a) Approximately normal because n <= 0.05N and np(1-p) < 10. b) Not normal because n <= 0.05 and np(1-p) >= 10. c) Not normal because n <= 0.05 and np(1-p) < 10. d) Approximately normal because n <= 0.05N and np(1-p) >= 10. B) Determine the mean of the sampling distribution of p^ (round to two decimal places as needed). C) Determine the standard deviation of the sampling distribution of p^ (round to three decimal places as needed). In the random sample of 800 adults, what is the probability that less than 16% have no credit cards? (round to four decimal places as needed). E) Would it be unusual if a random sample of 800 adults results in 152 or more having no credit cards? a) The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%. b) The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is less than 5%. c) The result is unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%. d) The result is unusual because the probability that p^ is greater than or equal to this sample proportion is less than 5%.

Explanation / Answer

n = 800 , p = 0.17

a) np = 800*0.17 = 136>10

n(1-p) = 800*0.83 = 664 > 10

d) Approximately normal because n <= 0.05N and np(1-p) >= 10 is correct

b) mean of p^ = p = 0.17

c) sd (p^) = sqrt(pq/n) = sqrt(0.17*0.83/800) = 0.013280624 = 0.013

d)

P(p^< 0.16)

Z= (p^ - 0.17)/0.013280624

P(Z<(0.16 -0.17)/0.013280624)

=P(Z< -0.75297666)

= 0.2257

e) 152/800 = 0.19

P(p^ > 0.19)

=

P(Z > (0.19 -0.17)/0.013280624)

=P(Z > 1.50595)

= 0.066

since 0.066 > 0.05

a) The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%. is correct

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