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? 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.

Answer 1

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.