Homework SourseConsider the following competing hypotheses and accompanying
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2.
Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Calculate the critical value at the 10% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
No, since the value of the test statistic is not less than the critical value.
Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Calculate the critical value at the 10% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
| Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2. |
| H0: 1 2 0 |
| HA: 1 2 < 0 |
Solution
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2.
H0: 1 2 0
HA: 1 2 < 0
formula43.mml = 243 formula44.mml = 264
s1 = 25 s2 = 26
n1 = 13 n2 = 13
This is a lower tail test.
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.1
Population 1 Sample
Sample Size
13
Sample Mean
243
Sample Standard Deviation
25
Population 2 Sample
Sample Size
13
Sample Mean
264
Sample Standard Deviation
26
Intermediate Calculations
Population 1 Sample Degrees of Freedom
12
Population 2 Sample Degrees of Freedom
12
Total Degrees of Freedom
24
Pooled Variance
650.5000
Standard Error
10.0038
Difference in Sample Means
-21.0000
t Test Statistic
-2.0992
Lower-Tail Test
Lower Critical Value
-1.3178
p-Value
0.0232
Reject the null hypothesis
a-1.
Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. -2.10
(Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
a-2.
Calculate the critical value at the 10% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) -1.318
a-3. Do you reject the null hypothesis at the 10% level?
Yes, since the value of the test statistic is not less than the critical value.
No, since the value of the test statistic is less than the critical value.
Yes, since the value of the test statistic is less than the critical value.
No, since the value of the test statistic is not less than the critical value.
b-1.
Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.1
Population 1 Sample
Sample Size
13
Sample Mean
243
Sample Standard Deviation
25.0000
Population 2 Sample
Sample Size
13
Sample Mean
264
Sample Standard Deviation
26.0000
Intermediate Calculations
Numerator of Degrees of Freedom
10015.3905
Denominator of Degrees of Freedom
417.9492
Total Degrees of Freedom
23.9632
Degrees of Freedom
23
Standard Error
10.0038
Difference in Sample Means
-21.0000
Separate-Variance t Test Statistic
-2.0992
Lower-Tail Test
Lower Critical Value
-1.3195
p-Value
0.0235
Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. -2.10
(Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
b-2.
Calculate the critical value at the 10% level of significance. (Negative value should be indicated by a minus sign. -1.320 Round your answer to 3 decimal places.)
b-3. Do you reject the null hypothesis at the 10% level?
Yes, since the value of the test statistic is not less than the critical value.
Yes, since the value of the test statistic is less than the critical value.
No, since the value of the test statistic is not less than the critical value.
No, since the value of the test statistic is less than the critical value.
| Pooled-Variance t Test for the Difference Between Two Means | |
| (assumes equal population variances) | |
| Data | |
| Hypothesized Difference | 0 |
| Level of Significance | 0.1 |
| Population 1 Sample | |
| Sample Size | 13 |
| Sample Mean | 243 |
| Sample Standard Deviation | 25 |
| Population 2 Sample | |
| Sample Size | 13 |
| Sample Mean | 264 |
| Sample Standard Deviation | 26 |
| Intermediate Calculations | |
| Population 1 Sample Degrees of Freedom | 12 |
| Population 2 Sample Degrees of Freedom | 12 |
| Total Degrees of Freedom | 24 |
| Pooled Variance | 650.5000 |
| Standard Error | 10.0038 |
| Difference in Sample Means | -21.0000 |
| t Test Statistic | -2.0992 |
| Lower-Tail Test | |
| Lower Critical Value | -1.3178 |
| p-Value | 0.0232 |
| Reject the null hypothesis |
