You want to determine if your widgets from machine 1 are the same as machine 2.

Question

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

Explanation / Answer

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

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