An article discussed the opening of a Market. The following data compared the prices of some kitchen staples at the new Market (group 1) and at the old Market (group 2) located 15 blocks away. ITEM                                      GROUP 1                           GROUP 2 HALF GALLON MILK 16.8 22.0 DOZEN EGGS 11.7 15.2 ORANGE JUICE (64OZ) 15.6 18.7 HEAD OF LETTUCE 16.7 15.6 1LB GROUND BEEF 17.5 20.8 6OZ TUNA 18.1 19.5 1LB APPLES 14.1 17.0 LINGUINI 21.8 19.5 SALMON STEAK 1LB 13.9 16.5 WHOLE CHICKEN PER LB 20.8 24.0 A. Use the math symbol to formulate null hypothesis and alternative hypothesis to test whether there is evidence that the mean price is lower at GROUP 1 than at GROUP 2. B. At the 0.01 level of significance, what is the value of the test statistic? What is the critical value? What is the degree of freedom? Using the critical value approach, is there evidence that the mean price is lower at GROUP 1 than at GROUP 2? What is your conclusion?

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An article discussed the opening of a Market. The following data compared the prices of some kitchen staples at the new Market (group 1) and at the old Market (group 2) located 15 blocks away.

ITEM                                      GROUP 1                           GROUP 2

HALF GALLON MILK 16.8 22.0
DOZEN EGGS 11.7 15.2
ORANGE JUICE (64OZ) 15.6 18.7
HEAD OF LETTUCE 16.7 15.6
1LB GROUND BEEF 17.5 20.8
6OZ TUNA 18.1 19.5
1LB APPLES 14.1 17.0
LINGUINI 21.8 19.5
SALMON STEAK 1LB 13.9 16.5
WHOLE CHICKEN PER LB 20.8 24.0

A. Use the math symbol to formulate null hypothesis and alternative hypothesis to test whether there is evidence that the mean price is lower at GROUP 1 than at GROUP 2.

B. At the 0.01 level of significance, what is the value of the test statistic? What is the critical value? What is the degree of freedom? Using the critical value approach, is there evidence that the mean price is lower at GROUP 1 than at GROUP 2? What is your conclusion?

Expert Solution
Step 1

It is given that the prices of some kitchen staples at the new market and the old market.

Part A)

The claim is that the mean price is lower at GROUP 1 than at GROUP 2.

Hypotheses:

Null hypothesis: H0: µ1 – µ2 = 0.

Alternative hypothesis: H1: µ1 – µ2 < 0.

Therefore, the test is left-tailed.

Step 2

Part B)

Given that the Level of significance is 0.01.

Calculations:

Calculate the mean and standard deviation for group 1 and group 2 using Excel is as follows:

Group 1:

Statistics homework question answer, step 2, image 1

Group 2:

Statistics homework question answer, step 2, image 2

Test statistic:

Calculate the test statistic is as follows:

Statistics homework question answer, step 2, image 3

Therefore, the value of test statistic is –1.6342.

 

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