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According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of n = 350 adults is obtained from the city. Describe the sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. O A. Approximately normal; µ, = 0.34, o, = 0.001 O B. Binomial; u, = 119, o, = 8.862 O C. Exactly normal; 4, = 0.34, o, = 0.025 O D. Approximately normal; µ, = 0.34, o, = 0.025

According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of n = 350 adults is obtained from the city. Describe the sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. O A. Approximately normal; µ, = 0.34, o, = 0.001 O B. Binomial; u, = 119, o, = 8.862 O C. Exactly normal; 4, = 0.34, o, = 0.025 O D. Approximately normal; µ, = 0.34, o, = 0.025

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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According to a study conducted in one​ city, 34​% of adults in the city have credit card debts of more than​ $2000. A simple random sample of n equals 350 adults is obtained from the city. Describe the sampling distribution of Modifying Above p with caret​, the sample proportion of adults who have credit card debts of more than​ $2000. Round to three decimal places when necessary.

 

**Understanding Sampling Distribution of Proportions** According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of \( n = 350 \) adults is obtained from the city. Describe the sampling distribution of \( \hat{p} \), the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. **Options:** - **A.** Approximately normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.001 \) - **B.** Binomial; \( \mu_{\hat{p}} = 119 \), \( \sigma_{\hat{p}} = 8.862 \) - **C.** Exactly normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.025 \) - **D.** Approximately normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.025 \) **Analysis:** The distribution type and parameters of \( \hat{p} \) are important statistical considerations. For a sufficiently large sample size, the sampling distribution of a proportion \( \hat{p} \) can be approximated by a normal distribution. - **Mean (\( \mu_{\hat{p}} \))**: The mean of the sampling distribution of \( \hat{p} \) is the population proportion, 0.34. - **Standard Deviation (\( \sigma_{\hat{p}} \))**: Calculated using the formula \( \sqrt{\frac{p(1-p)}{n}} \). Given these calculations, we find that the standard deviation rounds to 0.025, making option **D** the correct description of the sampling distribution: approximately normal with \( \mu_{\hat{p}} = 0.34 \) and \( \sigma_{\hat{p}} = 0.025 \).
Transcribed Image Text:**Understanding Sampling Distribution of Proportions** According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of \( n = 350 \) adults is obtained from the city. Describe the sampling distribution of \( \hat{p} \), the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. **Options:** - **A.** Approximately normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.001 \) - **B.** Binomial; \( \mu_{\hat{p}} = 119 \), \( \sigma_{\hat{p}} = 8.862 \) - **C.** Exactly normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.025 \) - **D.** Approximately normal; \( \mu_{\hat{p}} = 0.34 \), \( \sigma_{\hat{p}} = 0.025 \) **Analysis:** The distribution type and parameters of \( \hat{p} \) are important statistical considerations. For a sufficiently large sample size, the sampling distribution of a proportion \( \hat{p} \) can be approximated by a normal distribution. - **Mean (\( \mu_{\hat{p}} \))**: The mean of the sampling distribution of \( \hat{p} \) is the population proportion, 0.34. - **Standard Deviation (\( \sigma_{\hat{p}} \))**: Calculated using the formula \( \sqrt{\frac{p(1-p)}{n}} \). Given these calculations, we find that the standard deviation rounds to 0.025, making option **D** the correct description of the sampling distribution: approximately normal with \( \mu_{\hat{p}} = 0.34 \) and \( \sigma_{\hat{p}} = 0.025 \).
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