According to a survey in a country, 37% of adults do not have any credit cards.

Question

According to a survey in a country, 37% of adults do not have any credit cards. Suppose a simple random sample of 500 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 describes the shape of the sampling distribution of ^p below.

___Approx. normal because n0.05N and np (1-p) <10.

___Not normal because n0.05N and np (1-p) 10.

___Not normal because n0.05N and np (1-p) <10.

___Approx. normal because n0.05N and np (1-p) 10.

Determine the mean of the sampling distribution of (phat) p ______. (round to two decimal places as needed)

Determine the standard deviation of the sampling distribution of (phat) p_____ (round to two decimal places as needed)

(b) In a random sample of 500 adults, what is the probability that less than 35% have no credit cards?

The probability is ______. (round to four decimal places as needed)

(c) Would it be unusual if a random sample of 500 adults results in 210 or more having no credit cards?

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

___ The result is unusual because the probability that ^p is greater than or equal to this sample proportion is greater than 5%.

___ The result is unusual because the probability that ^p is greater than or equal to this sample proportion is less than 5%.

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

Explanation / Answer

According to a survey in a country, 37% of adults do not have any credit cards. Suppose a simple random sample of 500 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 describes the shape of the sampling distribution of ^p below.

___Approx. normal because n0.05N and np (1-p) <10.

___Not normal because n0.05N and np (1-p) 10.

___Not normal because n0.05N and np (1-p) <10.

___Approx. normal because n0.05N and np (1-p) 10.

Determine the mean of the sampling distribution of (phat) p   0.37. (round to two decimal places as needed)

Determine the standard deviation of the sampling distribution of (phat) p 0.02 (round to two decimal places as needed)

Sd=sqrt(0.37*0.63/500) =0.0216

(b) In a random sample of 500 adults, what is the probability that less than 35% have no credit cards?

The probability is    0.1587. (round to four decimal places as needed)

Z value for 35%, z=(0.35-0.37)/0.02 =-1

P( z <-1) = 0.1587

(c) Would it be unusual if a random sample of 500 adults results in 210 or more having no credit cards?

P=210/500=0.42

Z value for 0.42 z=(0.42-0.37)/0.02 =2.5

P( z >2.5) = 0.0062

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

___ The result is unusual because the probability that ^p is greater than or equal to this sample proportion is greater than 5%.

___ The result is unusual because the probability that ^p is greater than or equal to this sample proportion is less than 5%.

___ 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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