Question

In: Statistics and Probability

The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can...

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? Use this information to solve the following questions.

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

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)

Ocean Rio Ranch
89 128
115 110
93 81
79 126
113 82
77 114
51 93
75 40
118 94
105 45
106 84
91 71
54 74
63 92
121 66
53 69
81 100
115 114
67 113
53 107
69 62
95 77
121 80
88 107
64 90
129
105
124

Show all work with all formulas.

Solutions

Expert Solution

Let X :- Average number of cars in Ocean drive lot.

Y :- Average number of cars in Rio Rancho lot.

To Test :-

H0 :-  

H1 :-

C. What is alpha for this analysis?

level of significance

D. What is the most appropriate test for this problem?

t-Test: Two-Sampled Assuming Equal Variances

Ocean ( X ) Rio ( Y )
89 7.6176 128 1293.4309
115 827.1376 110 322.7161
93 45.6976 81 121.7867
79 52.4176 126 1153.5737
113 716.0976 82 100.7153
77 85.3776 114 482.4305
51 1241.8576 93 0.9299
75 126.3376 40 2707.7141
118 1008.6976 94 3.8585
105 351.9376 45 2212.3571
106 390.4576 84 64.5725
91 22.6576 71 442.5007
54 1039.4176 74 325.2865
63 540.0976 92 0.0013
121 1208.2576 66 677.8577
53 1104.8976 69 530.64
81 27.4576 100 63.4301
115 827.1376 114 482.4305
67 370.1776 113 439.5019
53 1104.8976 107 223.9303
69 297.2176 62 902.1433
95 76.7376 77 226.0723
121 1208.2576 80 144.8581
88 3.0976 107 223.9303
64 494.6176 90 4.1441
2156 13178.56 129 1366.3595
105 168.0731
124 1021.7165
Total 2577 15706.965

Mean

Standard deviation

Mean

Standard deviation

Test Statistic :-





t = -0.885

Test Criteria :-
Reject null hypothesis if


Result :- Fail to Reject Null Hypothesis

Lower bound critical value

Upper bound critical value

Conclusion :- Accept Null Hypothesis   

There is no statistical difference in the mean number of cars in the two lots

P value = 2 * P ( t > - 0.885 ) = 0.3803

Decision based on P value

Reject null hypothesis if P value < level of significance.

P value = 0.3803 > 0.01, hence we fail to reject null hypothesis.


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