Question

Determine if the average price of items at two grocery stores is different. To answer this question, you will take a sample of the same 20 items at both stores and use this information to perform the appropriate hypothesis test.

Which test (the two-sample t-test or paired t-test) is appropriate for this problem based on how the data were collected?

How the data are entered into an Excel spreadsheet depends on whether it is more appropriate to use the two-sample t-methods or the paired t-methods:

1. Entering data into an Excel spreadsheet: How should the date be entered in Excel?

2. Which of the following is the most appropriate hypothesis test to use in this problem: paired test or two-sample test? Why?

3. Do you feel it is appropriate to use the t-methods for this problem? Why or why not? c. Do you feel the null hypothesis will be rejected based on your graphical display? Why or why not?

Answer 1

In the given problem our aim is to determine whether the average price of items at two grocery stores is different. For this purpose we are asked to take a sample of the same 20 items from each stores.

1. Since we are taking the prices of each 20 different items from 2 different stores we could use paired t test. We can collect the same 20 commodities from the two stores and indicate the prices of each commodities as in the given table:

Commodity	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T
Store 1	15	24	16	25	34	47	38	55	47	35	46	28	25	45	43	30	28	16	10	38
Store 2	17	25	17	27	36	47	39	55	48	36	46	30	27	46	46	30	29	18	12	40

2. We could enter the data into excel by taking Store 1 as the title for the first column and enter the values in the same order as given in the table and store 2 as the second column. The excel sheet with the above data entered is attached below.

2. The most appropriate test here is paired t test itself because for doing this type of comparison it is necessary to take the same commodities from the 2 stores so in this case paired samples is most appropriate and so the appropriate test is paired t test.

3. Here the hypothesis could be

H₀ : there is no significant difference between the means. ie;

v/s

H₁ : there is significant difference between the means. ie;

where is the mean of the store 1 and is the mean of the store 2.

After entering the data

DATA DATA ANALYSIS t test ; paired Two sample for Means

enter the variable 1 range with the store 1 data and variable 2 range with store 2 data enter hypothesized mean difference as 0 and give a tick mark to the labels column.

According to our data the output will be as follows:

So we can use by this method and take decisions on whether to accept or reject the null hypothesis

If p value less than 0.05 we reject

and t stat < P critical two tail.

In our example we reject the null hypothesis.