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(a) Describe the sampling distribution of 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 p below. O A. Not normal because ns0.05N and np(1- p) 2 10 B. Not normal because ns0.05N and np(1 – p) < 10 C. Approximately normal because ns0.05N and np(1- p) < 10 O D. Approximately normal because ns0.05N and np(1- p) 2 10 Determine the mean of the sampling distribution of p. | (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of 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.)

(a) Describe the sampling distribution of 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 p below. O A. Not normal because ns0.05N and np(1- p) 2 10 B. Not normal because ns0.05N and np(1 – p) < 10 C. Approximately normal because ns0.05N and np(1- p) < 10 O D. Approximately normal because ns0.05N and np(1- p) 2 10 Determine the mean of the sampling distribution of p. | (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of 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.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 7: a, b, c, and d. 

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. **(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.)
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. **(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.)
**Transcription of Probability and Statistical Analysis** 1. **Random Sampling of Adults Without Credit Cards:** - If we obtain 100 different random samples of 300 adults, we would expect a certain number of samples to result in more than 22% not owning a credit card. - **Instruction:** Round to the nearest integer as needed. 2. **Calculation of Probability:** - What is the probability that in a random sample of 300 adults, the percentage of those who do not own a credit card falls between 17% and 22%? - **Answer Field:** The probability is _____. - **Instruction:** Round to four decimal places as needed. 3. **Interpretation of Probability:** - If 100 different random samples of 300 adults were obtained, one would expect a certain number of samples to fall between 17% and 22% not owning a credit card. - **Instruction:** Round to the nearest integer as needed. 4. **Evaluation of Unusual Results:** - Query: 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? - **Answer Options:** - **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%. - **Instruction:** Round to four decimal places as needed. **Note:** Replace blanks and placeholders with the actual computed numbers to complete the transcription based on statistical calculations.
Transcribed Image Text:**Transcription of Probability and Statistical Analysis** 1. **Random Sampling of Adults Without Credit Cards:** - If we obtain 100 different random samples of 300 adults, we would expect a certain number of samples to result in more than 22% not owning a credit card. - **Instruction:** Round to the nearest integer as needed. 2. **Calculation of Probability:** - What is the probability that in a random sample of 300 adults, the percentage of those who do not own a credit card falls between 17% and 22%? - **Answer Field:** The probability is _____. - **Instruction:** Round to four decimal places as needed. 3. **Interpretation of Probability:** - If 100 different random samples of 300 adults were obtained, one would expect a certain number of samples to fall between 17% and 22% not owning a credit card. - **Instruction:** Round to the nearest integer as needed. 4. **Evaluation of Unusual Results:** - Query: 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? - **Answer Options:** - **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%. - **Instruction:** Round to four decimal places as needed. **Note:** Replace blanks and placeholders with the actual computed numbers to complete the transcription based on statistical calculations.
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