Paired two sample t-test for a difference of two means Q11.1 • Name:

. Prices for commonly purchased products were obtained in two different stores. Is there average price difference? If there is a difference in the mean price, is that difference statistically significant?

Note that where possible, products that were the same size from the same company were compared. Where this was not possible, products which were the same size from different companies were used. In three instances the sizes were different, in these cases the prices were adjusted using the ratio of the product weights.

This form of study is a called a "market basket" price survey. Note that only a few items are sampled. The TTEST study is run to see if the differences in the average price, if any, are likely to be reproduced in a larger selection of items from the stores. Prices were gathered on .

Product Ace Commercial Palm Terrace
Crisco shortening 16 oz 6.30 2.55
Tomato ketchup (Western, Heinz) 3.75 3.15
Sapporo ichiban ramen (case) 17.00 17.50
Corned beef (Ox Palm, Hormel) 3.95 7.35
Tuna, canned (Coco, Bumblebee) 2.00 1.75
Spam, regular 3.95 3.95
Folgers coffee 33.9 oz 21.95 20.45
Condensed milk (Lucky cow, Hosen) 1.85 1.29
Colgate, Total 5.75 7.60
Kellogg Fruit Loops cereal 4.25 7.35
Dial Gold soap three pack 4.50 3.25
  1. ____________________________ Which store do you think has lower prices, Ace Commercial or Palm Terrace?
  2. ___________ Calculate the sample mean x product price for Ace Commercial.
  3. ___________ Calculate the sample mean x product price for Palm Terrace.
  4. __________________ Is there an average price difference?
  5. __________________ What is the p-value? Use the TTEST function for the difference of means for paired data with two tails to determine the p-value for this paired two sample data.
  6. __________________ Is the difference in the means statistically significant at a risk of a type I error alpha α = 0.05?
  7. __________________ Would we fail to reject | or | reject a null hypothesis of no difference in the sample means?
  8. ____________________________ Which store, if any, has statistically significantly lower prices on average, Ace Commercial, Palm Terrace, or neither?