A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05. (a) A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean standard deviation (b) Is the sampling distribution of p approximately normal for random samples of size n = 100? Explain. (c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean standard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p? If not, explain why not. (Select all that apply.) O When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases. When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.
A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05. (a) A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean standard deviation (b) Is the sampling distribution of p approximately normal for random samples of size n = 100? Explain. (c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean standard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p? If not, explain why not. (Select all that apply.) O When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases. When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.
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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![**Educational Website Transcript:**
A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.
(a) A random sample of \( n = 100 \) people will be selected from this population and \( \hat{p} \), the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of \( \hat{p} \)? (Round your standard deviation to four decimal places.)
- Mean: [______]
- Standard deviation: [______]
(b) Is the sampling distribution of \( \hat{p} \) approximately normal for random samples of size \( n = 100 \)? Explain.
(c) Suppose that the sample size is \( n = 400 \) rather than \( n = 100 \). What are the values for the mean and standard deviation when \( n = 400 \)? (Round your standard deviation to four decimal places.)
- Mean: [______]
- Standard deviation: [______]
**Does the change in sample size affect the mean and standard deviation of the sampling distribution of \( \hat{p} \)? If not, explain why not. (Select all that apply.)**
- [ ] When the sample size increases, the mean increases.
- [ ] When the sample size increases, the mean decreases.
- [ ] When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.
- [ ] When the sample size increases, the standard deviation increases.
- [ ] When the sample size increases, the standard deviation decreases.
- [ ] When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f11b0a5-f758-48c2-911f-774d5e291a60%2F0feb602a-02a1-4b6b-a29b-71520477888e%2F28ao17s_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcript:**
A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.
(a) A random sample of \( n = 100 \) people will be selected from this population and \( \hat{p} \), the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of \( \hat{p} \)? (Round your standard deviation to four decimal places.)
- Mean: [______]
- Standard deviation: [______]
(b) Is the sampling distribution of \( \hat{p} \) approximately normal for random samples of size \( n = 100 \)? Explain.
(c) Suppose that the sample size is \( n = 400 \) rather than \( n = 100 \). What are the values for the mean and standard deviation when \( n = 400 \)? (Round your standard deviation to four decimal places.)
- Mean: [______]
- Standard deviation: [______]
**Does the change in sample size affect the mean and standard deviation of the sampling distribution of \( \hat{p} \)? If not, explain why not. (Select all that apply.)**
- [ ] When the sample size increases, the mean increases.
- [ ] When the sample size increases, the mean decreases.
- [ ] When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.
- [ ] When the sample size increases, the standard deviation increases.
- [ ] When the sample size increases, the standard deviation decreases.
- [ ] When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.
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