Question

Problem 3: Food Prices: Target versus Safeway.  Grocery prices of the same randomly selected items were collected and compared from Target and Safeway.  Imagine you were interested in conducting a hypothesis test to determine whether the mean prices were significantly different.  Note: to answer the questions below, subtract Target price – Safeway price (i.e. subtract Safeway price from Target price).

Data:

Mean = -0.5071, Standard Deviation = 0.9012

Ball Park Hot Dogs	3.79	3.79	0
Milk Gallon	2.79	2.99	-0.2
Tomato Sauce 16 oz.	0.42	0.49	-0.07
Grape Tomato	0.99	1.29	-0.3
Chicken Breast	4.79	3.39	1.4
Lays Chips	3.14	3.99	-0.85
Coco Puffs	2.99	3.75	-0.76
Brand Cereal	2.39	3.09	-0.7
Special K	2.99	3.95	-0.96
Foldgers	4.39	4.69	-0.3
String Cheese	4.64	3.99	0.65
Sharp Cheddar	2.54	4.79	-2.25
Trop. Orange Juice	3.59	4.89	-1.3
Water 24 pack	5.09	5.19	-0.1
Pampers Diapers	6.49	8.49	-2
Coke 2L	4.99	5.19	-0.2
Ground Beef	3.69	3.5	0.19
Bacon 16 oz	5.29	7.69	-2.4
Mac n Cheese	1.22	1.05	0.17
Corn	0.82	0.89	-0.07
Ranch Dressing	1.92	2.99	-1.07
Rice	2.24	1.99	0.25
Baby Carrot	1.59	1.59	0
Strawberries 16 oz	2.69	3.99	-1.3

1. Construct a 95% confidence interval using the above data.  Please do this “by hand” using the formula and showing your work (please type your work).  Use your t-table (found in the last page of our formula packet) to obtain your t* critical value needed for the confidence interval.  Present this confidence as (lower limit, upper limit).

3. Imagine you were using a hypothesis test to determine if a significant difference exists in mean price between the two stores (the hypotheses would be H₀: m_D= 0 vs H_a: m_D≠0).  What conclusion can be made in this case using only your confidence interval? Provide an answer and a reason for your choice in one or two sentences.  Again, please only use your confidence interval to answer this question (i.e. do not run this hypothesis test).

Answer 1