(d) Would it be unusual for a random sample of 300 adults to result in 51 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. (Round to four decimal places as needed.) O A. The result is not unusual because the probability that p is less than or equal to the sample proportion is , which is greater than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is, which is less than 5%. OC. The result is unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O D. The result is unusual because the probability that p is less than or equal to the sample proportion is which is greater than 5%.
(d) Would it be unusual for a random sample of 300 adults to result in 51 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. (Round to four decimal places as needed.) O A. The result is not unusual because the probability that p is less than or equal to the sample proportion is , which is greater than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is, which is less than 5%. OC. The result is unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O D. The result is unusual because the probability that p is less than or equal to the sample proportion is which is greater than 5%.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
PART D ONLY
![### Statistical Analysis of Credit Card Ownership
#### Probability and Random Samples
**(a)** If 100 different random samples of 300 adults were obtained, one would expect [ ] to result in more than 22% not owning a credit card.
*(Round to the nearest integer as needed.)*
**(c)** What is the probability that in a random sample of 300 adults, between 17% and 22% do not own a credit card?
The probability is [ ].
*(Round to four decimal places as needed.)*
**Interpret this probability:**
If 100 different random samples of 300 adults were obtained, one would expect [ ] to result in between 17% and 22% not owning a credit card.
*(Round to the nearest integer as needed.)*
#### Unusual Events in Sampling
**(d)** Would it be unusual for a random sample of 300 adults to result in 51 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.
*(Round to four decimal places as needed.)*
- **A.** The result is not unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is greater than 5%.
- **B.** The result is not unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is less than 5%.
- **C.** The result is unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is less than 5%.
- **D.** The result is unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is greater than 5%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00e5d0fd-d29d-4158-acae-9d363981be4a%2F89225d9c-61d1-4761-9368-a77228e620e2%2F5pmw6e_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Credit Card Ownership
#### Probability and Random Samples
**(a)** If 100 different random samples of 300 adults were obtained, one would expect [ ] to result in more than 22% not owning a credit card.
*(Round to the nearest integer as needed.)*
**(c)** What is the probability that in a random sample of 300 adults, between 17% and 22% do not own a credit card?
The probability is [ ].
*(Round to four decimal places as needed.)*
**Interpret this probability:**
If 100 different random samples of 300 adults were obtained, one would expect [ ] to result in between 17% and 22% not owning a credit card.
*(Round to the nearest integer as needed.)*
#### Unusual Events in Sampling
**(d)** Would it be unusual for a random sample of 300 adults to result in 51 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.
*(Round to four decimal places as needed.)*
- **A.** The result is not unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is greater than 5%.
- **B.** The result is not unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is less than 5%.
- **C.** The result is unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is less than 5%.
- **D.** The result is unusual because the probability that \( \hat{p} \) is less than or equal to the sample proportion is [ ], which is greater than 5%.
![According to a survey in a country, 19% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) Describe the sampling distribution of \( \hat{p} \), 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 \( \hat{p} \) below.
- A. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \)
- B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \)
- C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \)
- D. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \)
Determine the mean of the sampling distribution of \( \hat{p} \).
\( \mu_{\hat{p}} = \) [ ] (Round to two decimal places as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\( \sigma_{\hat{p}} = \) [ ] (Round to three decimal places as needed.)
(b) What is the probability that in a random sample of 300 adults, more than 22% do not own a credit card?
The probability is [ ].
(Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00e5d0fd-d29d-4158-acae-9d363981be4a%2F89225d9c-61d1-4761-9368-a77228e620e2%2F3iqin1p_processed.png&w=3840&q=75)
Transcribed Image Text:According to a survey in a country, 19% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) Describe the sampling distribution of \( \hat{p} \), 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 \( \hat{p} \) below.
- A. Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \)
- B. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \)
- C. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \)
- D. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \)
Determine the mean of the sampling distribution of \( \hat{p} \).
\( \mu_{\hat{p}} = \) [ ] (Round to two decimal places as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\( \sigma_{\hat{p}} = \) [ ] (Round to three decimal places as needed.)
(b) What is the probability that in a random sample of 300 adults, more than 22% do not own a credit card?
The probability is [ ].
(Round to four decimal places as needed.)
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