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
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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