Problem 1.


Three supermarket chains in the Denver area each claim to have the lowest overall prices. As part of an investigative study on supermarket advertising, the Denver Daily News conducted a study. First, a random sample of nine grocery items was selected. Next, the price of each selected item was checked at each of the three chains on the same day. Use 0.05 level of significance.


Item Super$ Ralph's Lowblaws
1 $1.21 $1.20 $1.70
2 1.41 1.10 1.12
3 1.27 1.79 2.80
4 2.22 2.90 2.23
5 2.04 2.01 2.03
6 4.40 4.23 4.51
7 5.50 4.59 5.50
8 4.86 4.31 4.76
9 5.25 5.64 5.68

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What is the decision rule for both? (Round your answer to 2 decimal places.)


For Stores, reject H0 if F > _________
For Items, reject H0 if F > _________



Problem 2.

In an ANOVA table MSE was equal to 10. Random samples of six were selected from each of four populations, where the sum of squares total was 250.


(b) What is the decision rule? Use the .05 significance level. (Round your answer to 2 decimal places.)

Reject H0 if F> _________

You will need to determine degrees of freedom, then check an ANOVA table for level of significance. If the F-ratio exceeds the critical value from the table, then the null (H0) will be rejected.

To find the decision rule for both problems, we need to use the F-distribution and the significance level of 0.05.

Problem 1:
In this problem, we are comparing the prices of the same nine grocery items at three different supermarket chains. We need to determine if there is a significant difference in prices between the three chains.

To find the decision rule, we need to calculate the critical value for F based on the degrees of freedom and the significance level. The degrees of freedom for the numerator (denoted as df1) is the number of groups or chains minus one, which is 3 - 1 = 2. The degrees of freedom for the denominator (denoted as df2) is the total number of observations minus the number of groups, which is 9 - 3 = 6.

We can use a statistical table or a calculator to find the critical value for F. For a significance level of 0.05 and df1 = 2 and df2 = 6, the critical value is approximately 5.14.

Therefore, the decision rule for the supermarkets is: Reject H0 (null hypothesis) if the calculated F-value is greater than 5.14.

Problem 2:
In this problem, an ANOVA table is given with the Mean Square Error (MSE) equal to 10. We are testing for a significant difference between four populations.

To find the decision rule, we need to calculate the critical value for F based on the degrees of freedom and the significance level. The degrees of freedom for the numerator (denoted as df1) is the number of groups or populations minus one, which is 4 - 1 = 3. The degrees of freedom for the denominator (denoted as df2) is the total number of observations minus the number of groups, which is 4 * 6 - 4 = 20.

Using a statistical table or a calculator, we find that for a significance level of 0.05 and df1 = 3 and df2 = 20, the critical value is approximately 3.10.

Therefore, the decision rule for ANOVA test is: Reject H0 if the calculated F-value is greater than 3.10.