Module # 7 Review: Confidence Interval Estimation And introduction to Fundamental of hypothesis testing

 

1. x̄ = 85 and σ = 8, and n = 64, set up a 95% confidence interval estimate of the population mean μ.

85 ± 1.96 = 85-1.96= 83.04 and 85+1.96= 86.96

 

 

2. If x̄ = 125, σ = 24 and n = 36, set up a 99% confidence interval estimate of the population mean μ.

125±10.32= 125-10.32= 114.68 and 125+10.32=135.32

 

3. The manager of a supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. It is known from the manufacturer’s specification sheet that standard deviation of the amount of paint is equal to 0.02 gallon. A Random sample of 50 cans is selected and the sample mean amount of paint per 1 gallon is 0.99 gallon.

 

3a. Set up a 99% confidence interval estimate of the true population mean amount of paint included in 1-gallon can?

 

0.02/50

= 0.99±2.58 * 0.02/50

.99-0.0004=0.9896.           .99+0.0004=0.9904

 
3b. On the basis of your results, do you think that the manager has a right to complain to the manufacturer? why?

Yes, because the CI does not equal to 1.

 

 

4. A stationery store wants to estimate the mean retail value of greeting cards that has in its inventory. A random sample of 20 greeting cards indicates an average value of $1.67 and standard deviation of $0.32

4a. Assuming a normal distribution set up with 95% confidence interval estimate of the mean value of all greeting cards stored in the store’s inventory.

 

x̄= 1.67      1.96*0.32/√20= 1402

 

 

1.67-0.1402= 1.5298. and 1.67+0.1402= 1.8102

 
4b. How might the results obtained in (a) be useful in assisting the store owner to estimate of the mean value of all greeting cards in the store’s inventory.

 

It lets the manager know that the inventory value is between $1.53 and $1.81

 

5. If you want to be 95% confident of estimating the population mean to within a sampling error of ± 5 and standard deviation is assumed to be equal 15, what sample size is required?

 

1.96 * 15/5

5.88

N=35

 

 

 

6. Generate your own null and alternative hypothesis statements and provide rationale for your selection.

 

Null example: Not doing the homework assignments will result in the student not passing the class.

 

Alternative example: Doing the homework has no effect on your final grade in the class.