1_A special bumper was installed on selected vehicles in a large fleet. The dollar cost of body repairs was recorded for all vehicles that were involved in accidents over a 1-year period. Those with the special bumper are the test group and the other vehicles are the control group, shown below. Each "repair incident" is defined as an invoice (which might include more than one separate type of damage).

Statistic Test Group Control Group

Mean Damage x1 = $ 1,101 x2 = $ 1,766

Sample Standard Deviation s1 = $ 696 s2 = $ 838

Repair Incidents n1 = 12 n2 = 9

Construct a 90 percent confidence interval for the true difference of the means assuming equal variances. 90% confidence level means the two tails sum up to 10%, therefore each tail = .05

Your total degrees of freedom will be (n1-1) + (n2-1) = _____

Please use Excel Formula: =T.INV(probability,total degrees of freedom) to come up with the answer:

=T.INV(probability,df) = _________

2_Below is a random sample of shoe sizes for 12 mothers and their daughters. Please copy the data to an Excel worksheet.

Calculate the mean and standard deviation for the difference:

Size/Daughter/Mother/Difference

1 8 7 1

2 8 7 1

3 7.5 7.5 0

4 8 8 0

5 9 8.5 0.5

6 9 8.5 0.5

7 8.5 7.5 1

8 9 7.5 1.5

9 9 6 3

10 8 8 0

11 7 7 0

12 8 7 1

Please use Excel formulas to determine:

MEAN =AVERAGE(DIFFERENCE COLUMN) = ____________

STANDARD DEVIATION =STD.DEV.S(DIFFERENCE COLUMN) = _____

3_On the above example, find the right option for Ho: 0 versus Ha: > 0. Use = .01 therefore probability = 1 - .01 = .99

Find the t-critical value using Excel formula =T.INV(Probability,degrees of freedom) where n = 12 and df = n-1

=T.INV(Probability,df) =______________

4_Based on the above data, on the Data Analysis Tookpak in Excel, please run a t-Test: Paired Two Sample for Means (Variable 1: Daughter's column and Variable 2: Mother's column). Please determine the following:

What is the t-statistical value: ________________

5_Based on the above data, on the Data Analysis Tookpak in Excel, please run a t-Test: Paired Two Sample for Means (Variable 1: Daughter's column and Variable 2: Mother's column). Please determine the following:

What is the p-value for 1-tail: ________________.

https://openstax.org/books/introductory-business-statistics/pages/10-5-two-population-means-with-known-standard-deviationsLinks to an external site.