Question

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.
3. The test-statistic for this data =  (Please show your answer to three decimal places.)
   
4. The p-value for this sample = (Please show your answer to four decimal places.)
   
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.

Answer 1

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.