Question

Context: You own three Chick-Fil-A franchises. In your sales district, you know that the average weekly sales are $542,000. One of your stores (Clarkesville store) brought in an average of $530,000 each week in the last year.

Assume that you conducted the most appropriate test and found the following:

Z = 3.32

Lower Critical Value = -2.00

Upper Critical Value = 2.00

P-value = 0.0015

Level of significance = 0.05

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1a) Based on this information, which of the following best describes the conclusions that you could draw from this test?

a) There is no statistically significant difference between the average weekly sales for my sales district and the average weekly sales of the Clarkesville store.

b) The average weekly sales in the sales district is statistically higher than the average weekly sales of the Clarkesville store.

c) The average weekly sales in the sales district is statistically lower than the average weekly sales of the Clarkesville store.

d) There is a statistically significant difference between the average weekly sales for my sales district and the average weekly sales of the Clarkesville store.

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Context: You suspect that there may be a difference not only between the stores, but also between sales on rainy and sunny days. In fact, you think that rainy days in Clayton product higher sales because there are few indoor activities for children in the area and the restaurant fills up with families playing in the play area when it rains.

1b) What test could you use to determine if there are statistically significant differences in sales a) based on your 3 store locations, b) based on rainy/sunny weather and c) based on an interaction between the location and weather?

a) Chi-square

b) Two way ANOVA

c) One way ANOVA

d) Correlation

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Context...Use this for the next two questions: You want to know if there is a correlation between the number of promotions being run and the weekly sales in one of your restaurants. You suspect that the promotions are bringing in customers and increasing your weekly sales. Over a year, you collect information about how many promotions are being run and the sales for each week (sample of 52 weeks).

1c) What test could you use to determine if there is a relationship between promotions and sales?

a) One sample hypothesis test

b) Two way ANOVA

c) One way ANOVA

d) Correlation

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1d) Assume that you conducted the most appropriate test and found the following:

R = 0.92

Based on this information, which of the following best describes the conclusions that you could draw from this test?

a) There is no relationship between the number of promotions and the weekly sales.

b) There is a weak relationship between the number of promotions and the weekly sales.

c) There is a moderate relationship between the number of promotions and the weekly sales.

d) There is a strong relationship between the number of promotions and the weekly sales.

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Context: Piedmont is interested in the success of its students and wants to know what the high achievers have in common. The administration believes that those who study more and who had high GPAs in high school are more likely to be successful. Likewise, they want to rule out any differences in success by gender and race.

1e) Which test would you use to determine if there is a relationship between the number of hours studied and GPA?

a) One sample hypothesis test

b) Two way ANOVA

d) Chi-square

e) Correlation

Answer 1

(1a) Option (d) There is a statistically significant difference between the average weekly sales for my sales district and the average weekly sales of the Clarkesville store.

> This is a two-tailed test. As p-value is less than the level of significance, we reject the null hypothesis and conclude that there is a statistically significant difference.

(1b) Option (b) Two way ANOVA.

> As there are two subjects to compare with there interaction term, this is a two way anova test.

(1c) Option (d) Correlation.

> To test the relationship between two variables, we use correlation test.

(1d) Option (d) There is a strong relationship between the number of promotions and the weekly sales.

> The correlation coefficient, r is high enough for 52 sample data points. So there id a strong relationship between them.

(1e) Option (e) Correlation.

> This is same relationship test as (1c).

Thank you...