An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within1.4years of the population mean. Assume the population of ages is normally distributed.(a) Determine the minimum sample size required to construct a90%confidence interval for the population mean. Assume the population standard deviation is1.6years.(b) The sample mean is20years of age. Using the minimum sample size with a90%level of confidence, does it seem likely that the population mean could be within9%of the sample mean? within10%of the sample mean? Explain.Click here to view page 1 of the Standard Normal Table.LOADING...Click here to view page 2 of the Standard Normal Table.LOADING... (b) The90%confidence interval is(18.0 18.0,22.0 22.0).It▼ does not seemseemslikely that the population mean could be within9%of the sample mean because the interval formed by the values9%away from the sample mean▼ entirely containsoverlaps but does not entirely containthe confidence interval. It▼ seemsdoes not seemlikely that the population mean could be within10%of the sample mean because the interval formed by the values10%away from the sample mean▼ entirely containsoverlaps but does not entirely containthe confidence interval.(Round to two decimal places as needed.)

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Answered: An admissions director wants to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

1.4

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

1.6

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

of the sample mean? within

10%

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.

(b) The

90%

confidence interval is

(18.0

18.0,

22.0

22.0).

▼

does not seem

seems

likely that the population mean could be within

of the sample mean because the interval formed by the values

away from the sample mean

▼

entirely contains

overlaps but does not entirely contain

the confidence interval. It

▼

seems

does not seem

likely that the population mean could be within

10%

of the sample mean because the interval formed by the values

10%

away from the sample mean

▼

entirely contains

overlaps but does not entirely contain

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 + ...

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