Answered: An admissions director wants to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

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I need help with stats/2023, sorry I keep submitting confidence intervals, but I am having internet and computer issues, I appreciate your help.

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within

1.6

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

1.8

years.

(b) The sample mean is

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

10%

of the sample mean? within

11%

of the sample mean? Explain.

A) The minimum sample size required to construct a 90% confidence interval is _____4_____ students.

B) The 90% confidence interval is (_______ , _________). It (1) does or does not, seem likely that the population mean could be within 9% of the sample mean because 9% off rom the sample mean would fall (2) inside or outside the confidence interval. It (3) does or does not, seem likely that the population mean could be within 10% of the sample mean because 10% off from the sample mean would fall (4) outside or inside the confidence interval.

(Round to 2 decimal places as needed)

Thank you

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 + ...

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