Homework SourseA researcher wished to compare the average daily hotel room
A researcher wished to compare the average daily hotel room rates between San Francisco and Los Angeles. The researcher obtained an SRS of 27 hotels in downtown San Francisco and found the sample mean X1=$156, with a standard deviation S1=$18. The researcher also obtained an independent SRS of 24 hotels in downtown Los Angeles and found the sample mean X2=$143, with a standard deviation S2=$10. Let U1 and U2 represent the mean cost of the populations of all hotels in these cities, respectively. Assume the two-sample t procedure are safe to use.
If we had used the more accurate software approximation to the degrees of freedom, we would have used which of the following for the number of degrees of freedom for the t procedure?
A. 23
B. 42
C. 26
D.40
Suppose the researcher had wished to test the hypotheses
Ho : u2, Ha: u1 > u2
Based on the more accurate software approximation of the degree of freedom, the exact P value for the hypothesis test is:
A. 0.0036
B. 0.0018
C. 0.0024
D. 0.0012
Solution
A researcher wished to compare the average daily hotel room rates between San Francisco and Los Angeles. The researcher obtained an SRS of 27 hotels in downtown San Francisco and found the sample mean X1=$156, with a standard deviation S1=$18. The researcher also obtained an independent SRS of 24 hotels in downtown Los Angeles and found the sample mean X2=$143, with a standard deviation S2=$10. Let U1 and U2 represent the mean cost of the populations of all hotels in these cities, respectively. Assume the two-sample t procedure are safe to use.
If we had used the more accurate software approximation to the degrees of freedom, we would have used which of the following for the number of degrees of freedom for the t procedure?
A. 23
B. 42
C. 26
D.40
Answer: B: 42
note: sotware result shows that DF=41.53. since 41 is not there, i rounded up.
Suppose the researcher had wished to test the hypotheses
Ho : u2, Ha: u1 > u2
Based on the more accurate software approximation of the degree of freedom, the exact P value for the hypothesis test is:
A. 0.0036
B. 0.0018
C. 0.0024
D. 0.0012
Answer: D: 0.0012
Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
1 Sample
Sample Size
27
Sample Mean
156
Sample Standard Deviation
18.0000
2 Sample
Sample Size
24
Sample Mean
143
Sample Standard Deviation
10.0000
Intermediate Calculations
Numerator of Degrees of Freedom
261.3611
Denominator of Degrees of Freedom
6.2933
Total Degrees of Freedom
41.5301
Degrees of Freedom
41
Standard Error
4.0208
Difference in Sample Means
13.0000
Separate-Variance t Test Statistic
3.2332
Upper-Tail Test
Upper Critical Value
1.6829
p-Value
0.0012
Reject the null hypothesis
| Separate-Variances t Test for the Difference Between Two Means | |
| (assumes unequal population variances) | |
| Data | |
| Hypothesized Difference | 0 |
| Level of Significance | 0.05 |
| 1 Sample | |
| Sample Size | 27 |
| Sample Mean | 156 |
| Sample Standard Deviation | 18.0000 |
| 2 Sample | |
| Sample Size | 24 |
| Sample Mean | 143 |
| Sample Standard Deviation | 10.0000 |
| Intermediate Calculations | |
| Numerator of Degrees of Freedom | 261.3611 |
| Denominator of Degrees of Freedom | 6.2933 |
| Total Degrees of Freedom | 41.5301 |
| Degrees of Freedom | 41 |
| Standard Error | 4.0208 |
| Difference in Sample Means | 13.0000 |
| Separate-Variance t Test Statistic | 3.2332 |
| Upper-Tail Test | |
| Upper Critical Value | 1.6829 |
| p-Value | 0.0012 |
| Reject the null hypothesis |
