Question

Suppose that you are responsible for making arrangements for a business convention and that you have been charged with choosing a city for the convention that has the least expensive rooms. You have narrowed your choices to Atlanta and Houston. The table containing samples of prices for rooms in Atlanta and Houston is provided in the Excel Online file below. Construct a spreadsheet to answer the following questions. Because considerable historical data on the prices of rooms in both cities are available, the population standard deviations for the prices can be assumed to be $19.88 in Atlanta and $27.2 in Houston.

Atlanta	Houston
85	65
115	145
60	80
110	80
105	100
80	145
105	115
115	140
85	140
105	120
60	85
95	150
65	120
70	120
125	115
80	110
110	95
115	130
95	90
95	75
125	150
115	105
70	110
85	120
105	75
120	70
75	135
70	115
105	55
95	140
90	135
125	110
75	60
115	105
115	70
	140
	120
	105
	95
	80

Population Standard Deviation

Atlanta 19.88

Houston 27.20

Level of Significance 0.05

Based on the sample data, can you conclude that the mean price of a hotel room in Atlanta is lower than one in Houston?

z-value	(to 2 decimals)
p-value	(to 4 decimals)

Answer 1

	Atlanta ( X )	Σ ( Xi- X̅ )2	Houston ( Y )	Σ ( Yi- Y̅ )2
	85	121	65	1838.2656
	115	361	145	1378.2656
	60	1296	80	777.0156
	110	196	80	777.0156
	105	81	100	62.0156
	80	256	145	1378.2656
	105	81	115	50.7656
	115	361	140	1032.0156
	85	121	140	1032.0156
	105	81	120	147.0156
	60	1296	85	523.2656
	95	1	150	1774.5156
	65.0	961	120	147.0156
	70	676	120	147.0156
	125	841	115	50.7656
	80	256	110	4.52
	110	196	95	165.7656
	115	361	130	489.5156
	95	1	90	319.5156
	95	1	75	1080.7656
	125	841	150	1774.5156
	115	361	105	8.2656
	70	676	110	4.5156
	85	121	120	147.0156
	105	81	75	1080.7656
	120	576	70	1434.5156
	75	441	135	735.7656
	70	676	115	50.7656
	105	81	55	2795.7656
	95	1	140	1032.0156
	90	36	135	735.7656
	125	841	110	4.5156
	75	441	60	2292.0156
	115	361	105	8.2656
	115	361	70	1434.5156
			140	1032.0156
			120	147.0156
			105	8.2656
			95	165.7656
			80	777.0156
Total	3360	13440	4315	28844.374

Mean X̅ = Σ Xi / n
X̅ = 3360 / 35 = 96

Mean Y̅ = ΣYi / n
Y̅ = 4315 / 40 = 107.875

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 < µ2

Test Statistic :-


Z = -2.18

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z( 0.05 ) = 1.645
Z < -Z(α) = 2.1758 < -1.645
Result :- Reject Null Hypothesis

P value = P ( Z < 2.18 ) = 0.0148
Looking for the value Z = -2.18 in standard normal table to find the P value.

There is sufficient evidence to support the claim that the mean price of a hotel room in Atlanta is lower than one in Houston.