A random sample of 35 transmission replacement costs find the mean to be $2680.0

Question

A random sample of 35 transmission replacement costs find the mean to be $2680.00. Assume the population standard deviation is $400.00. A 95% confidence interval for the population mean repair cost is (2547.5, 2812.5). Change the sample size to n = 70. Construct a 95% confidence interval for the population mean repair cost. Which confidence interval is wider? Explain. Construct a 95% confidence interval for the population mean repair cost. The 95% confidence interval is (, ). (Round to one decimal place as needed.)

Explanation / Answer

margin of error = z-score * standard error

= 1.96 * 400/sqrt(70)

= 93.71

=>

lower bound = 2680 - 93.7 = 2586.3

upper bound = 2680 + 93.7 = 2773.7

hence confidence interval is (2586.3 , 2773.7)

no, it is not wider , since we have more data , we narrow the interval , with higher confidence

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