Homework SourseYou want to determine if your widgets from machine 1 are the
You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 2,000.21 and a sample standard deviation 6.1 and a sample size of 2. Machine 2 has a sample mean of 1,998.76 and a sample standard deviation of 6.2 with a sample size of 2. With an alpha of .05 can we claim that there is a difference between the output of the two machines. Which of the following statements are true?
| A. We will reject the null hypothesis and prove there is a difference between the 2 populations | |
| B. We will not reject the null hypothesis and thus we can |
Solution
The appropriate answer is (B).
The results from the excel calculations are shown below:
| Pooled-Variance t Test for the Difference Between Two Means | |
| (assumes equal population variances) | |
| Data | |
| Hypothesized Difference | 0 |
| Level of Significance | 0.05 |
| Population 1 Sample | |
| Sample Size | 2 |
| Sample Mean | 2000.21 |
| Sample Standard Deviation | 6.1 |
| Population 2 Sample | |
| Sample Size | 2 |
| Sample Mean | 1998.76 |
| Sample Standard Deviation | 6.2 |
| Intermediate Calculations | |
| Population 1 Sample Degrees of Freedom | 1 |
| Population 2 Sample Degrees of Freedom | 1 |
| Total Degrees of Freedom | 2 |
| Pooled Variance | 37.825 |
| Standard Error | 6.1502 |
| Difference in Sample Means | 1.45 |
| t Test Statistic | 0.2358 |
| Two-Tail Test | |
| Lower Critical Value | -4.3027 |
| Upper Critical Value | 4.3027 |
| p-Value | 0.8356 |
| Do not reject the null hypothesis |
