Question

According to a survey in a​ country, 23​% of adults do not own a credit card....

According to a survey in a​ country, 23​% of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Complete parts​ (a) through​ (d) below.

a) Describe the sampling distribution of ModifyingAbove p with caretp​, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caretp below. A. Approximately normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10np(1−p)≥10 B. Not normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis less than 10np(1−p)<10 C. Approximately normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis less than 10np(1−p)<10 D. Not normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10np(1−p)≥10 Determine the mean of the sampling distribution of ModifyingAbove p with caretp. mu Subscript ModifyingAbove p with caret Baseline equalsμp=. 23 ​(Round to two decimal places as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caretp. sigma Subscript ModifyingAbove p with caretσpequals=. 0210 ​(Round to three decimal places as​ needed.) ​

(b) What is the probability that in a random sample of 400 ​adults, more than 26​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 400 adults were​ obtained, one would expect nothing to result in more than 26​% not owning a credit card. ​(Round to the nearest integer as​ needed.) ​

(c) What is the probability that in a random sample of 400 ​adults, between 21​% and 26​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 400 adults were​ obtained, one would expect nothing to result in between 21​% and 26​% not owning a credit card. ​(Round to the nearest integer as​ needed.)

​(d) Would it be unusual for a random sample of 400 adults to result in 84 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice

Homework Answers

Answer #1

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

Mean = 0.23

Standard deviation = 0.021

(b) The probability is 0.0770.

If 100 different random samples of 400 adults were​ obtained, one would expect 31 to result in more than 26​% not owning a credit card.

(c) The probability is 0.7521.

If 100 different random samples of 400 adults were​ obtained, one would expect 301 to result in between 21​% and 26​% not owning a credit card. ​

​(d) The p-value is 0.1709.

The result is not unusual.

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