A report on weekly grocery expenditures of Morehead State University claimed that the mean expenditure, for the students living off campus, was $65.00 with a standard deviation of $30 (That is, μ = 65 and σ = 30). A random sample of 36 MSU students shows a Sample Mean of $87 (x=87) and a standard deviation of 24 (S =24) on the weekly grocery expenditures of this sample of MSU students: Construct a 99% confidence interval for the value of the mean, by relying on the sample mean, but when you DO KNOW the value of the population standard deviation (which was 30). Assuming you have no knowledge of the population mean and standard deviation (that is, you are relying solely on your sample data), construct a 90% confidence interval for the value of the MSU students’ mean grocery expenditures based on the above sample’s information.(xand s). Given the information above regarding your sample values [ Remember, we said:, A random sample of 36 MSU students shows a Sample Mean of $87 (x=87)and a standard deviation of 24 (S=24) n=36), test, at α = 0.01, a hypotheses concerning the reliability of the above population information regarding the claimed grocery expenditures of the MSU undergraduate students (Claim: μ = 65), assuming you DO KNOW the standard deviation of the population (that is σ = 30). Do part c again, but, this time, assume you DO NOT know the standard deviation of the Population and your sample size is 25 (n = 25). Suppose you are concerned that the mean student grocery expenditures reported above may be under-estimated and you think it may more than 65 (That is, if the actual mean was below what has been claimed, you would have no concerns). Now, in this case, assume that another random sample of 81 MSU students showed a mean expenditures of $72. Conduct a hypothesis test, with α= 0.05, to check the validity of the claim made above (Claim: μ = 65).

Answered: A report on weekly grocery expenditures…

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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A report on weekly grocery expenditures of Morehead State University claimed that the mean expenditure, for the students living off campus, was $65.00 with a standard deviation of $30 (That is, μ = 65 and σ = 30).

A random sample of 36 MSU students shows a Sample Mean of $87 (x=87)

and a standard deviation of 24 (S =24) on the weekly grocery expenditures of this sample of MSU students:

Construct a 99% confidence interval for the value of the mean, by relying on the sample mean, but when you DO KNOW the value of the population standard deviation (which was 30).

Assuming you have no knowledge of the population mean and standard deviation (that is, you are relying solely on your sample data), construct a 90% confidence interval for the value of the MSU students’ mean grocery expenditures based on the above sample’s information.(xand s).

Given the information above regarding your sample values [ Remember, we said:, A random sample of 36 MSU students shows a Sample Mean of $87 (x=87)

and a standard deviation of 24 (S=24) n=36), test, at α = 0.01, a hypotheses concerning the reliability of the above population information regarding the claimed grocery expenditures of the MSU undergraduate students (Claim: μ = 65), assuming you DO KNOW the standard deviation of the population (that is σ = 30).

Do part c again, but, this time, assume you DO NOT know the standard deviation of the Population and your sample size is 25 (n = 25).

Suppose you are concerned that the mean student grocery expenditures reported above may be under-estimated and you think it may more than 65 (That is, if the actual mean was below what has been claimed, you would have no concerns). Now, in this case, assume that another random sample of 81 MSU students showed a mean expenditures of $72. Conduct a hypothesis test, with α= 0.05, to check the validity of the claim made above (Claim: μ = 65).

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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