A news article estimated that only 4% of those ages 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 ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.04. (a) A random sample of n = 100 people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.) meanstandard deviation (b) Is the sampling distribution of p̂ approximately normal for random samples of size n = 100? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10 (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.) meanstandard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p̂? 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. (d) Is the sampling distribution of p̂ approximately normal for random samples of size n = 400? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10

A news article estimated that only 4% of those ages 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 ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.04. (a) A random sample of n = 100 people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.) meanstandard deviation (b) Is the sampling distribution of p̂ approximately normal for random samples of size n = 100? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10 (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.) meanstandard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p̂? 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. (d) Is the sampling distribution of p̂ approximately normal for random samples of size n = 400? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Related questions

Question

(a)

A random sample of

n = 100

people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.)

meanstandard deviation

(b)

Is the sampling distribution of p̂ approximately normal for random samples of size

n = 100?

Explain. (Select all that apply.)

the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10

(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.)

meanstandard deviation

Does the change in sample size affect the mean and standard deviation of the sampling distribution of p̂? 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.

(d)

Is the sampling distribution of p̂ approximately normal for random samples of size

n = 400?

Explain. (Select all that apply.)