Question

A restaurant manager is interested in investigating whether the main course ordered and the dessert ordered...

A restaurant manager is interested in investigating whether the main course ordered and the dessert ordered are related. The table below shows the results of a survey.

Frequencies of Food Preference and Dessert Types
Fish Meat Vegetarian
Cake 91 99 48
Ice Cream 108 101 48
Pie 117 110 41

What can be concluded at the αα = 0.10 significance level?

1. What is the correct statistical test to use?
• Goodness-of-Fit
• Independence
• Homogeneity
• Paired t-test
2. What are the null and alternative hypotheses?
H0:H0:
• Main course and dessert are dependent.
• Main course and dessert are independent.
• The distribution of dessert orders is not the same for each main course that is ordered.
• The distribution of dessert orders is the same for each main course that is ordered.

H1:H1:
• Main course and dessert are independent.
• Main course and dessert are dependent.
• The distribution of dessert orders is not the same for each main course that is ordered.
• The distribution of dessert orders is the same for each main course that is ordered.
5. The p-value is Select an answer less than (or equal to) greater than  αα
6. Based on this, we should
• accept the null
• reject the null
• fail to reject the null
7. Thus, the final conclusion is...
• There is sufficient evidence to conclude that the distribution of dessert orders is the same for each main course that is ordered.
• There is sufficient evidence to conclude that the main course that is ordered and the dessert that is ordered are dependent.
• There is sufficient evidence to conclude that the main course that is ordered and the dessert that is ordered are independent.
• There is insufficient evidence to conclude that the distribution of dessert orders is the same for each main course that is ordered.
• There is insufficient evidence to conclude that the main course that is ordered and the dessert that is ordered are dependent.

The statistical software output for this problem is :

Independence

Main course and dessert are independent.

Main course and dessert are dependent.

The test-statistic for this data = 2.884

The p-value for this sample = 0.5774

The p-value is greater than  α

fail to reject the null

There is insufficient evidence to conclude that the distribution of dessert orders is the same for each main course that is ordered.

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