Question

Location A Location B Location C Location D

52                   75                  67                  58

59                   55                  77                  38

81                   95                  47                  82

63                   46                  74                  77

73                   85                  56                  91

1. Test the following hypotheses and also state the alternate hypothesis in each case. Write a sentence or two summarizing your conclusion after you have completed each hypothesis testing.

Hypothesis 1 The average time spent per table in Location A is the same as the average time spent per table in Location B.

Hypothesis 2 The average time spent per table in Location A is more than the average time spent per table in Location B.

Hypothesis 3 The average time spent per table in Location A is less than the average time spent per table in Location B.

Hypothesis 4 The average time spent per table in Location A is the same as the average time spent per table in Location C.

Hypothesis 5 The average time spent per table in Location A is the same as the average time spent per table in Location D.

Hypothesis 6 The average time spent per table in Location B is the same as the average time spent per table in Location C.

Hypothesis 7 The average time spent per table in Location B is the same as the average time spent per table in Location D.

Hypothesis 8 The average time spent per table in Location C is the same as the average time spent per table in Location D.

Hypothesis 9 The variance of time spent in Location A is the same as the variance of time spent in Location B.

Hypothesis 10 The variance of time spent in Location A is the same as the variance of time spent in Location C.

Hypothesis 11 The variance of time spent in Location A is the same as the variance of time spent in Location D.

Hypothesis 12 The variance of time spent in Location B is the same as the variance of time spent in Location C.

Hypothesis 13 The variance of time spent in Location B is the same as the variance of time spent in Location D.

Hypothesis 14 The variance of time spent in Location C is the same as the variance of time spent in Location D.

Hypothesis 15 The average time spent per table in ALL locations is exactly equal to each other. Hint: You will have to perform an ANOVA here.

4. Overall, what proporrtion of the tables are occupied for at least 75 mimutes? Construc a 95% confidence interval of the proportion of tables that are occupied for 75 minutes or more. HInt: Consult the materials on confidence interval for population proportion.
5. Write a short essay (no more than a page articulating the insight that you gained after doing the data analysis. What managerial action (if any) would you recommend based on your results?

Answer 1

Note : Allowed to solve one question per post. Solving the most difficult (Calculation intensive) Hypothesis 15 and additionally solving Solving the 95% confidence interval of the proportion.

Please post the remaining in a new post.

Hypothesis 15 The average time spent per table in ALL locations is exactly equal to each other. Hint: You will have to perform an ANOVA here.

Ho: The average time spent per table in ALL locations is exactly equal to each other
H1 : The average time spent per table in ALL locations is not exactly equal to each other

Since the pvalue is greater than 0.05, we fail to reject the null hypothesis and conclude that average time spent per table in ALL locations is exactly equal to each other

Overall, what proporrtion of the tables are occupied for at least 75 mimutes? Construc a 95% confidence interval of the proportion of tables that are occupied for 75 minutes or more. HInt: Consult the materials on confidence interval for population proportion.

We see that 8 out of 20 are at least 75 minutes.

Hence the proportion = 8/20 = 0.4

95% confidence interval of the proportion of tables that are occupied for 75 minutes or more