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A researcher wants to know if the average time in jail for robbery has increased from what it was when the average sentence was 7 years. he obtains data on 400 more-recent robberies and finds an average time served of 7.5 years. find a 95% confidence interval for the average time served (assume jail time follows a normal distribution with standard deviation 3 years).

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At 95% confidence interval, the z score is 1.96. Using the formula:

Confidence Interval = x ± z s / sqrt (n)

where x is the average time served, s is standard deviation and n is number of samples

 

Confidence interval = 7.5 ± (1.96 * 3) / sqrt (400)

Confidence interval = 7.5 ± 0.294

Confidence interval = 7.206 to 7.794

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