Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for the data are given in the table. Hotel C Hotel A Hotel B 155 17.7 180 115 Sample Average (s) Sample Standard Deviation 22.4 12.5 (a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A - Hotel B. Round your answers to two decimal places.) $ to s (b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B- Hotel C. Round your answers to two decimal places.) $ to s (c) Do the intervals in parts (a) and (b) contain the value (₁-₂)=0? O Yes, the interval in part (a) contains (₂-₂) = 0. O Yes, the interval in part (b) contains (₁-₂) = 0. O Yes, both intervals contain (#₁ - ₂) = 0. O No, neither interval contains (₁-H₂) = 0. Why is this of interest to the researcher? ○ If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0. If (H₂-H₂) = 0 is contained in the confidence interval, it is implied that we cannot conclude there is a difference in the average room rates for the two hotels. ○ If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0. If (H₂-H₂) = 0 is contained in the confidence interval, it is implied that there was an error in the database records. If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.
Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for the data are given in the table. Hotel C Hotel A Hotel B 155 17.7 180 115 Sample Average (s) Sample Standard Deviation 22.4 12.5 (a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A - Hotel B. Round your answers to two decimal places.) $ to s (b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B- Hotel C. Round your answers to two decimal places.) $ to s (c) Do the intervals in parts (a) and (b) contain the value (₁-₂)=0? O Yes, the interval in part (a) contains (₂-₂) = 0. O Yes, the interval in part (b) contains (₁-₂) = 0. O Yes, both intervals contain (#₁ - ₂) = 0. O No, neither interval contains (₁-H₂) = 0. Why is this of interest to the researcher? ○ If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0. If (H₂-H₂) = 0 is contained in the confidence interval, it is implied that we cannot conclude there is a difference in the average room rates for the two hotels. ○ If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0. If (H₂-H₂) = 0 is contained in the confidence interval, it is implied that there was an error in the database records. If (H₁-H₂) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Confidence Intervals and Room Rates Analysis**
Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for the data are given in the table.
| | Hotel A | Hotel B | Hotel C |
|----------------|---------|---------|---------|
| **Sample Average ($)** | 155 | 180 | 115 |
| **Sample Standard Deviation** | 17.7 | 22.4 | 12.5 |
---
**(a)** Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A - Hotel B. Round your answers to two decimal places.)
\[ \$ \_\_\_ \text{ to } \$ \_\_\_ \]
**(b)** Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B - Hotel C. Round your answers to two decimal places.)
\[ \$ \_\_\_ \text{ to } \$ \_\_\_ \]
**(c)** Do the intervals in parts (a) and (b) contain the value \((\mu_1 - \mu_2) = 0\)?
- \( \bigcirc \) Yes, the interval in part (a) contains \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) Yes, the interval in part (b) contains \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) Yes, both intervals contain \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) No, neither interval contains \((\mu_1 - \mu_2) = 0\).
**Why is this of interest to the researcher?**
- If \((\mu_1 - \mu_2) = 0\) is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.
- If \((\mu_1 - \mu_2) = 0\) is contained in the confidence interval, it is implied that we](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbff43673-f06b-43ca-b409-46eb420ace6b%2F26e77f19-a8b1-4eca-b53a-35cca3585ccb%2Fqdj83ps_processed.png&w=3840&q=75)
Transcribed Image Text:**Confidence Intervals and Room Rates Analysis**
Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for the data are given in the table.
| | Hotel A | Hotel B | Hotel C |
|----------------|---------|---------|---------|
| **Sample Average ($)** | 155 | 180 | 115 |
| **Sample Standard Deviation** | 17.7 | 22.4 | 12.5 |
---
**(a)** Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A - Hotel B. Round your answers to two decimal places.)
\[ \$ \_\_\_ \text{ to } \$ \_\_\_ \]
**(b)** Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B - Hotel C. Round your answers to two decimal places.)
\[ \$ \_\_\_ \text{ to } \$ \_\_\_ \]
**(c)** Do the intervals in parts (a) and (b) contain the value \((\mu_1 - \mu_2) = 0\)?
- \( \bigcirc \) Yes, the interval in part (a) contains \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) Yes, the interval in part (b) contains \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) Yes, both intervals contain \((\mu_1 - \mu_2) = 0\).
- \( \bigcirc \) No, neither interval contains \((\mu_1 - \mu_2) = 0\).
**Why is this of interest to the researcher?**
- If \((\mu_1 - \mu_2) = 0\) is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.
- If \((\mu_1 - \mu_2) = 0\) is contained in the confidence interval, it is implied that we
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