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# ANOVA and Hypothesis Testing on Specific Cases

See the attached file.

1. Consider the following data taken from a local grocery store, in which monthly sales of baked goods that were placed on different shelves was collected (bottom, middle, top shelves). Is there a difference in monthly sales between shelves? Please test this at a 5% probability level.
a. State the hypotheses.
b. State the decision rule.
c. Calculate the test statistic.
d. Make a decision and draw a conclusion.
e. If there is a significant difference found, what procedure would you use to determine where the differences in means lie?
i. Using MegaStat, calculate those comparisons.

Display Height
Bottom Middle Top
58.2 73.0 52.4
53.7 78.1 49.7
55.8 75.4 50.9
55.7 76.2 54.0
52.5 78.4 52.1
58.9 82.1 49.9

2. A marketing organization wants to study the effects of four sales methods on weekly sales of a product. The organization employs the following design in which three salesmen use each sales method. The results obtained are given in the table below. Is there a difference in sales methods or salesmen in weekly sales? (4 points)
a. State the hypotheses.
b. State the decision rule.
c. Calculate the test statistic.
d. Make a decision and draw a conclusion.

Sales Pressure Salesman
A B C
1 32 29 30
2 32 30 28
3 28 25 23
4 25 24 23

3. A telemarketing firm has studied the effects of two factors on the response to its television advertisements. The first factor is the time of day at which the ad is run, while the second factor is the position of the ad within the hour. The data presented below give the number of calls placed to an 800 number following a sample broadcast of the advertisement. Test for significant effects at the 5% level of probability. (8 points)
a. State the hypotheses.
b. State the decision rule.
c. Calculate the test statistic.
d. Make a decision and draw a conclusion.
e. Please graph and describe the interaction.

Hour Half-Hour Early Late
42 36 62 51
Morning 37 41 68 47
41 38 64 48
Time of 62 57 88 67
Day Afternoon 60 60 85 60
58 55 81 66
100 97 127 105
Evening 96 96 120 101
103 101 126 107.

#### Solution Preview

Please see the attachments.

1. Consider the following data taken from a local grocery store, in which monthly sales of baked goods that were placed on different shelves was collected (bottom, middle, top shelves). Is there a difference in monthly sales between shelves? Please test this at a 5% probability level.
a. State the hypotheses.
b. State the decision rule.
c. Calculate the test statistic.
d. Make a decision and draw a conclusion.
e. If there is a significant difference found, what procedure would you use to determine where the differences in means lie?
i. Using MegaStat, calculate those comparisons.

Display Height
Bottom Middle Top
58.2 73.0 52.4
53.7 78.1 49.7
55.8 75.4 50.9
55.7 76.2 54.0
52.5 78.4 52.1
58.9 82.1 49.9

a. State the hypotheses.

H0: There is no significant difference in the mean monthly sales between shelves.
H1: There is significant difference in the mean monthly sales between shelves.

b. State the decision rule.
Reject the null hypothesis, if the observed significance ( p value) is less than the significance level.

c. Calculate the test statistic.
ANOVA table
Source SS df MS F p-value
Treatment 2,273.880 2 1,136.9400 184.57 2.74E-11
Error 92.400 15 6.1600
Total 2,366.280 17

d. Make a decision and draw a conclusion
Since the p value is less than the significance level, we reject the null hypothesis. The sample provides enough evidence to support the claim that there is significant difference in the mean ...

#### Solution Summary

This solution conducts ANOVA and hypothesis testing on three cases by stating the null and alternative hypothesis. It compares the test statistic to the p-value to accept the null and alternative hypothesis with all steps shown.

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