In a large population, 46% of the households own VCR’s. A SRS of 100 households is...

In a large population, 46% of the households own VCR’s. A SRS of 100 households is to be contacted and asked if they own a VCR.

a. Let p^ be the sample proportion who say they own a VCR. find the mean of the sampling distribution of the sample proportion

b. Let p^ be the sample proportion who say they own a VCR. Find the standard deviation of the sampling distribution of the sample proportion

c. Let p^ be the sample proportion who say they own a VCR. Why is the sampling distribution of p^ approximately normal

d. What is the probability that more than 60 will own VCRs?

e. Let p^ be the sample proportion who say they own a VCR. If we decrease the sample size from 100 to 50 that would multiply the standard deviation of the sampling distribution by a factor of:

Solutions

Expert Solution

a. Let p^ be the sample proportion who say they own a VCR. find the mean of the sampling distribution of the sample proportion

The mean of the sampling distribution of the sample proportion = 0.46

b. Let p^ be the sample proportion who say they own a VCR. Find the standard deviation of the sampling distribution of the sample proportion

The standard deviation of the sampling distribution of the sample proportion = sqrt((0.46*(1-0.46))/100) = 0.045

c. Let p^ be the sample proportion who say they own a VCR. Why is the sampling distribution of p^ approximately normal

np = 100*0.46 = 46 >= 10

n(1-p) = 100*.54 = 54 >= 10

Thus, the sampling distribution of p^ is approximately normal.

d. What is the probability that more than 60 will own VCRs?

The test statistic = 0.60-0.46/sqrt(0.46*(1-0.46)/100) = 2.81

The probability is 0.0025.

e. Let p^ be the sample proportion who say they own a VCR. If we decrease the sample size from 100 to 50 that would multiply the standard deviation of the sampling distribution by a factor of:

The standard deviation of the sampling distribution will be multiplied by a factor of 4.

orchestra answered 2 years ago

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