Concept explainers
Hotel Costs Refer to Exercise 8.20. The
a. Find a 95% confidence interval for the difference in the average room rates for the Marriott and the Westin hotel chains.
b. Find a 99% confidence interval for the difference in the average room rates for the Westin and the Doubletree hotel chains.
c. Do the intervals in parts a and b contain the value Why is this of interest to the researcher?
d. Do the data indicate a difference in the average room rates between the Marriott and the Westin chains? Between the Westin and the Doubletree chains?
(a)
To find: the 95% confidence interval for the difference between two population means.
Answer to Problem 8.51E
The confidence interval is
Explanation of Solution
Given:
The sample size of Region 1 (
The sample size of Region 2 (
The level of significance (
The sample mean of region 1 is 150.
The sample mean of region 2 is 165.
The sample variance of region 1 is 17.2.
The sample variance of region 2 is 22.5.
Formulae used:
Consider two sample sizes
Calculations:
Consider,
Also, Consider
The Z Critical value at 95% level of significance is 1.96 calculated from the standard normal table.
The
Therefore, the confidence interval for difference between two population means (
(b)
To find: the 99% confidence interval for the difference between two population means.
Answer to Problem 8.51E
The confidence interval is
Explanation of Solution
Given:
The sample size of Region 1 (
The sample size of Region 2 (
The level of significance (
The sample mean of region 1 is 165.
The sample mean of region 2 is 125.
The sample variance of region 1 is 22.5.
The sample variance of region 2 is 12.8.
Calculations:
The Z Critical value at 99% level of significance is 2.58 calculated from the standard normal table.
The
Therefore, the confidence interval for difference between two population means (
(c)
To check: if there exists difference between two population means or not..
Answer to Problem 8.51E
Yes, there is a difference between two means.
Explanation of Solution
The confidence interval for difference between two population means (
The confidence interval for difference between two population means (
Since, 0 is not contained in either of the intervals.
Therefore, there is a significant difference in both the population means.
(d)
To check: if there exists difference between two population means or not.
Answer to Problem 8.51E
Yes, there is a difference between two means.
Explanation of Solution
The confidence interval for difference between two population means (
The confidence interval for difference between two population means (
Since, 0 is not contained in either of the intervals.
Therefore, there is a significant difference in both the population means.
This shows that there does exist significant rates difference.
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Chapter 8 Solutions
Introduction to Probability and Statistics
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill