A random sample of 45 ransmission replacement oosts find the mean to be $2510.00

Question

A random sample of 45 ransmission replacement oosts find the mean to be $2510.00 Assume the population slandand deviation is S425.00. A90Scondence intervail for the population ean repair cost is (3eos a2e4a Charge the sample size to n.90 Construd a 90% confidence nenalfor the populaton mean reparoost.michoondence nras-deepe Construct a0%conddence interval forthe population mean ar cost The 90% oorfidenoe interval is(1 Round to one decimal place as needed.) Which con idence interval is wider? Explain. Choose the cormect answer below O A The n-90 confidence interval is wider becouse a larger sample is taken, giving moneinformation about the population about the population interval is wider because a smaler sample is taken, giving less informeticn ere the same size because the confidence interval is based on the level of confidence and population standard deviation O B. The n 45 confidence i Cick to seiect your answertls MacBook Air 20p 4 2 3

Explanation / Answer

At 90% confidence interval the critical value is +/- 1.645

For n = 90

The confidence interval is

Mean +/- z0.05 * sd / sqrt (n)

= 2510 +/- 1.645 * 425/sqrt(90)

= 2510 +/- 73.694

= 2436.306, 2583.694

So for n = 45 sample size, t Confidence interval is more wider.

Option-B is the correct answer.

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