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...

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:

1. 
   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).
   

1. 
   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).
   
   

1. 
   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).

1. 
   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).

1. 
   
   
   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).