Question

A traveler wanted to know if the prices of hotels are different in the ten cities that he visits the most often. The list of the cities with the corresponding hotel prices for his two favorite hotel chains is in the table below. Test at the 1% level of significance.

Cities	Hyatt Regency prices in dollars	Hilton prices in dollars
Atlanta	107	169
Boston	358	289
Chicago	209	299
Dallas	209	198
Denver	167	169
Indianapolis	179	214
Los Angeles	179	169
New York City	625	459
Philadelphia	179	159
Washington, DC	245	239

What is the p-value? Round answer to four decimal places (i.e. 0.1234)? Answer

What is your decision? Answerreject the null hypothesisaccept the null hypothesisfail to reject the null hypothesis

Answer 1

(1) Hypothesis Test for 2 Means - 2 Tails

Let be the population average price at the Hyatt.

Let be the population average price at the Hilton.

From the given Data: Calculations are done at the end

For Hyatt: = 245.7, s₁ = 148.3, n₁ = 10

For Hilton: = 236.4, s₂ = 93, n₂ = 10

Since s₁/s₂ =148.3/93 = 1.59 (it lies between 0.5 and 2) we used the pooled variance.

Since we use the pooled variance, the degrees of freedom = n1 + n2 - 2 = 10 + 10 - 2 = 18

The Hypothesis:

H0: - = 0: The average price at the Hyatt is equal to the average price at the Hilton.

Ha: - 0: The average price at the Hyatt is different from the average price at the Hilton.

This is a Two tailed test.

The Test Statistic:

The p Value: The p value (2 Tail) for t = 0.132,df = 18,is; p value = 0.8685

The Critical Value: The critical value (2 tail) at = 0.01, df = 18; ,tcritical = +2.878 and -2.878

The Decision Rule:

The Critical Value Method: If tobserved is > tcritical or if tobserved is < -tcritical, Then Reject H0.

By the p value method: If the P value is < , Then Reject H0

The Decision:

The Critical Value Method: Since t observed (0.168) lies in between +2.878 and -2.878, We Fail to Reject H0.

By the p value method: Since P value (0.8685) is > (0.01), We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 99% significance level to conclude that the average price at the Hyatt is different from the average price at the Hilton.

________________________________________________________________________

Calculations for the mean and the standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

#	X	Mean	(x - mean)2		#	X	Mean	(x - mean)2
1	107	245.700	19237.690		1	169	236.400	4542.760
2	358	245.700	12611.290		2	289	236.400	2766.760
3	209	245.700	1346.890		3	299	236.400	3918.760
4	209	245.700	1346.890		4	198	236.400	1474.560
5	167	245.700	6193.690		5	169	236.400	4542.760
6	179	245.700	4448.890		6	214	236.400	501.760
7	179	245.700	4448.890		7	169	236.400	4542.760
8	625	245.700	143868.490		8	459	236.400	49550.760
9	179	245.700	4448.890		9	159	236.400	5990.760
10	245	245.700	0.490		10	239	236.400	6.760
Total	2457.00		197952.1		Total	2364.00		77838.4

	Hyatt	Hilton
n	10	10
Sum	2457	2364
Average	245.70	236.4
SS(Sum of squares)	197952.1	77838.4
Variance = SS/n-1	21994.67778	8648.711111
Std Dev=Sqrt(Variance)	148.3	93.00