An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.2 years of the population mean. Assume the population of ages is normally distributed. (a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.4 years. (b) The sample mean is 21 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 8% of the sample mean? within 9% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. (a) The minimum sample size required to construct a 90% confidence interval is students. (Round up to the nearest whole number.) (b) The 90% confidence interval is O.). It V seem likely that the population mean could be within 8% of the sample mean because 8% off from the sample mean would fall v the confidence interval. It V seem likely that the population mean could be within 9% of the sample mean because 9% off from the sample mean would fall V the confidence interval. (Round to two decimal places as needed.)

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​The full question for part B is written down below. 

(b) The 90​% confidence interval is (​__,__​). It does/does not seem likely that the population mean could be within 8​% of the sample mean because 8​% off from the sample mean would fall outside/inside the confidence interval. It does not/does seem likely that the population mean could be within 9​% of the sample mean because 9​% off from the sample mean would fall outside/inside the confidence interval.

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.2 years of the population mean. Assume the population of ages is normally distributed.
(a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.4 years.
(b) The sample mean is 21 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 8% of the sample mean? within 9% of the sample mean? Explain.
Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table.
(a) The minimum sample size required to construct a 90% confidence interval is
students.
(Round up to the nearest whole number.)
(b) The 90% confidence interval is (, ). It
seem likely that the population mean could be within 8% of the sample mean because 8% off from the sample mean would fall
the confidence interval. It
seem likely
that the population mean could be within 9% of the sample mean because 9% off from the sample mean would fall
the confidence interval.
(Round to two decimal places as needed.)
Transcribed Image Text:An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.2 years of the population mean. Assume the population of ages is normally distributed. (a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.4 years. (b) The sample mean is 21 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 8% of the sample mean? within 9% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. (a) The minimum sample size required to construct a 90% confidence interval is students. (Round up to the nearest whole number.) (b) The 90% confidence interval is (, ). It seem likely that the population mean could be within 8% of the sample mean because 8% off from the sample mean would fall the confidence interval. It seem likely that the population mean could be within 9% of the sample mean because 9% off from the sample mean would fall the confidence interval. (Round to two decimal places as needed.)
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