Question

The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can accommodate up to 125 cars and the one on Rio Rancho can accommodate up to 130 cars. City planners are considering both increasing the size of the lots and changing the fee structure. To begin, the Planning Office would like some information on the number of cars in the lots at various times of the day. A junior planner officer is assigned the task of visiting the two lots at random times of the day and evening and counting the number of cars in the lot. The study lasted over a period of one month. Below is the number of cars in the lots for 25 visits of the Ocean Drive lot and 28 visits of the Rio Rancho lot. Assume the population standard deviation is equal and use an alpha value of 0.01 to determine if it is reasonable to conclude that there is a difference in the mean number of cars in the two lots?

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test for this problem? (choose one of the following)

a. t-Test: Paired Two Sample for Means

b. t-Test: Two-Sampled Assuming Equal Variances

c. t-Test: Two-Sample Assuming Unequal Variances

d. z-Test: Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. It is reasonable to conclude that there is a difference in the mean number of cars in the two lots? (choose one of the following) a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

Answer 1

A. What is the null hypothesis statement for this problem?

H₀: μ₁ = μ₂

B. What is the alternative hypothesis statement for this problem?

H₁: μ1 ≠ μ₂

C. What is alpha for this analysis?

0.01

D. What is the most appropriate test for this problem? (choose one of the following)

b. t-Test: Two-Sampled Assuming Equal Variances

E. What is the value of the test statistic for the most appropriate analysis?

Test Statistic:
t = (x1 - x2)/SQRT[(s1²/n1 + s2²/n2)/]
t = (86.24 - 92.04)/(sqrt((23.43²/25)+(24.12²/28))
t = -0.885

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

lower = =T.INV(0.005,51)

= -2.6757

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

upper = 2.6757

H. It is reasonable to conclude that there is a difference in the mean number of cars in the two lots? (choose one of the following)

b. No

I. What is the p-value for this analysis?

0.38031