Question

The selling price (in $) for the deluxe and standard model Ryobi wood sanders are shown for a sample of eight retail stores. Does the data suggest the difference in average selling price of these Ryobi models is more than $10 at alpha=.1

Retail Store Deluxe Standard

1 32 19

2 31 19

3 31 19

4 31 19

5 44 31

6 42 30

7 39 27

8 32 22

For the hypothesis stated above (in terms of Deluxe-Standard)

Question 1: What is the test statistic

Question 2: What is the conclusion

Question 3: What is the p value? Fill in only one of the following statements: If the z table is appropriate, p value = If t table is appropriate, Pvalue is between what two values

I understand that it is t problem as sigma is unknown. I am having a problem determining degrees of freedom and test statistic

Answer 1

This is a question of paired t test.

First we find difference of each pair of observation denoted as d​​​​​​i​​​.

Then we find mean and S​​​​​​2 for the d​​​​​​i​​​​​di

Then Our test statistic is based on this d as

t= d​​​​​​bar/(S/√n) and follows students t distribution with degrees of freedom =n-1=7.

Here n=8

Also our hypothesis is

Null: d=10

Alternate: d>10.

Test statistic is calculated as t=36.65

Corresponding p value for the test is 0.0001 which is much less than alpha =0.1 so we reject the null hypothesis and conslude that sample data suggests the difference in selling price is more than $10.

Calculation is given below.