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(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans...

(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans age 12 or older had been a victim of crime. The size of the sample was 6,4,00.

a) Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. Write a sentence explaining the meaning of this confidence interval.

b) Estimate the percentage of victims at the 99% confidence level. Write a sentence explaining the meaning of this confidence interval.

Imagine that the Sample size was cut in half to 3,200, but the survey found the same value of 17.0% for the percentage of victims.

c) Would the 95% confidence interval increase or decrease? By how much?

d) Would the 99% confidence interval increase or decrease? By how much?

Solutions

Expert Solution

a)

Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.161<p<0.179, which indicates that we are 95% confident that the true population proportion p is contained by the interval (0.161, 0.179).

b)

c)

the 95% confidence interval width increase and Increased by 0.008.

d) the 99% confidence interval width increases and increased by 0.01

milcah answered 1 year ago
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