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We would to conduct an analysis of variance at the 5% level of significance to compare the

mean delivery time for five different branches of a restaurant in the city.

We take a random sample of 7 measurements from the branch in St. Vital, 11

measurements from St. Boniface, 9 measurements from Transcona, 10 measurements from

Fort Rouge, and 8 measurements from Fort Garry.

We will assume for this test that delivery times for each branch follow a Normal

distribution.

The ANOVA table (with some values missing) is given below:

Sum of

Squares

Source of

Variation

Groups

Еггог

Total

df

2288.80

Mean Square

199.08

F/nPart (f) [2 marks]

The mean delivery times for Transcona and St. Vital, as well as the standard deviations, are

given below:

Branch

Transcona

St. Vital

Mean

32.29

27.89

Stdev

6.32

7.39

Calculate a 95% confidence interval for the true mean delivery time for Transcona. Also,

provide an interpretation of the confidence interval.

Do this work separately on paper.

Part (g) [2 marks]

Use the information above to calculate a 95% confidence interval for the difference in the

mean delivery times for Transcona and St. Vital (PTranscona St. Vital). Also, provide an

interpretation of the confidence interval.

Do this work separately on paper./nPart (a) [1 mark]

What are the hypotheses for the appropriate test of significance?

Do this work separately on paper.

Part (b) [3 marks]

Find all missing values in the table above. Show your calculations and display the final

complete ANOVA table.

Do this work separately on paper.

Part (c) [1 mark]

What is the P-value for the appropriate test of significance?

Do this work separately on paper.

Part (d) [1 mark]

Provided a fully-worded conclusion for this test.

Do this work separately on paper.

Part (e) [2 marks]

Suppose you had used the critical value method to conduct the test. What would be the

decision rule and the conclusion?

Do this work separately on paper.

Part (f) [2 marks]

The mean delivery times for Transcona and St. Vital, as well as the standard deviations, are

given below:

Branch

Transcona

St. Vital

Mean

32.29

27.89

Stdev

6.32

7.39

Fig: 1

Fig: 2

Fig: 3