Homework SourseA sample of 40 observations is selected from one population
A sample of 40 observations is selected from one population with a population standard deviation of 3.9. The sample mean is 102.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.2. The sample mean is 101.0. Conduct the following test of hypothesis using the 0.05 significance level.
State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
| A sample of 40 observations is selected from one population with a population standard deviation of 3.9. The sample mean is 102.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.2. The sample mean is 101.0. Conduct the following test of hypothesis using the 0.05 significance level. |
| H0 : 1 = 2 |
| H1 : 1 2 |
Solution
A sample of 40 observations is selected from one population with a population standard deviation of 3.9. The sample mean is 102.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.2. The sample mean is 101.0. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : 1 = 2
H1 : 1 2
a. This is a (Click to select)two-tailed test.
b.
State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
The decision rule is to reject H0 if z is (Click to select) outside the interval (-1.96, 1.96 ).
c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic = 1.32
d. What is your decision regarding H0?
(Click to select)Do not reject H0.
e. What is the p-value? (Round your answer to 4 decimal places.)
p-value = 0.1867
Z Test for Differences in Two Means
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
40
Sample Mean
102
Population Standard Deviation
3.9
Population 2 Sample
Sample Size
53
Sample Mean
101
Population Standard Deviation
3.2
Intermediate Calculations
Difference in Sample Means
1
Standard Error of the Difference in Means
0.7573
Z Test Statistic
1.3205
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.1867
Do not reject the null hypothesis
| Z Test for Differences in Two Means | |
| Data | |
| Hypothesized Difference | 0 |
| Level of Significance | 0.05 |
| Population 1 Sample | |
| Sample Size | 40 |
| Sample Mean | 102 |
| Population Standard Deviation | 3.9 |
| Population 2 Sample | |
| Sample Size | 53 |
| Sample Mean | 101 |
| Population Standard Deviation | 3.2 |
| Intermediate Calculations | |
| Difference in Sample Means | 1 |
| Standard Error of the Difference in Means | 0.7573 |
| Z Test Statistic | 1.3205 |
| Two-Tail Test | |
| Lower Critical Value | -1.9600 |
| Upper Critical Value | 1.9600 |
| p-Value | 0.1867 |
| Do not reject the null hypothesis |
