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.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...