The U.S. Census Bureau reported that in 2015 the proportion of adult Americans, ages 25 and older, who have a bachelor's degree or higher is 0.325.† Consider the population of all adult Americans, ages 25 and over, in 2015 and define p̂ to be the proportion of people in a random sample from this population who have a bachelor's degree or higher. (a) Would p̂ based on a random sample of only 10 people from this population have a sampling distribution that is approximately normal? Explain why or why not. , the sampling distribution of p̂ based on a random sample of size 10 residents approximately normally distributed because np is 10. (b) What are the mean and standard deviation of the sampling distribution of p̂ if the sample size is 600? (Round your standard deviation to four decimal places.) mean standard deviation (c) Suppose that the sample size is n = 300 rather than n = 600. What are the values for the mean and standard deviation when n = 300? (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 decreases, the mean increases. When the sample size decreases, the mean decreases. When the sample size decreases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size decreases, the standard deviation increases. When the sample size decreases, the standard deviation decreases. When the sample size decreases, 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.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...

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The U.S. Census Bureau reported that in 2015 the proportion of adult Americans, ages 25 and older, who have a bachelor's degree or higher is 0.325.† Consider the population of all adult Americans, ages 25 and over, in 2015 and define p̂ to be the proportion of people in a random sample from this population who have a bachelor's degree or higher.

(a)

Would p̂ based on a random sample of only 10 people from this population have a sampling distribution that is approximately normal? Explain why or why not.

, the sampling distribution of p̂ based on a random sample of size 10 residents approximately normally distributed because np is 10.

(b)

What are the mean and standard deviation of the sampling distribution of p̂ if the sample size is 600? (Round your standard deviation to four decimal places.)

mean

standard deviation

(c)

Suppose that the sample size is

n = 300

rather than

n = 600.

What are the values for the mean and standard deviation when

n = 300?

(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 decreases, the mean increases.

When the sample size decreases, the mean decreases.

When the sample size decreases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.

When the sample size decreases, the standard deviation increases.

When the sample size decreases, the standard deviation decreases.

When the sample size decreases, 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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