- You will examine the examine scores for the two training centers, using spreadsheet data – ExamScore.xlsx. The label Center A is in Cell A1 and the label Center B is in cell B1. The examination scores for Center A are in cells A2:A31 and examination scores for Center B are in cells B2:B41. The population standard deviations are assumed known with , and . The excel routine will request the input of variances which are , and . The following steps can be used to conduct a hypothesis test about the difference between the two population means.(20 points)

**Step 1**. Click the **Data** tab on the Ribbon

**Step 2**. In the **Analysis** group, click **Data Analysis**

**Step 3**. When the Data Analysis dialog box appears:

Choose **z-Test: Two Sample for Means**

**Step 4. **When the z-Test: Two Sample for Means dialog box appears:

Enter A1:A31 in the **Variable 1 Range** box

Enter B1:B41 in the **Variable 2 Range** box

Enter 0 in the **Hypothesized Mean Difference** box

Enter 100 in the **Variable 1 Variance (Known)** box

Enter 100 in the **Variable 2 Variance (Known)** box

Select **Labels**

Enter .05 in the **Alpha** box

Select **Output Range** and enter C1 in the box

Click **OK**

**Interpret the results from this hypothesis test using at least 50 words, providing discussions on whether exam scores for the two training centers are statistically equal or not. **

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- You will show how analysis of variance could be used to test for the equality of k population means using data: Chemitech.xlsx. You are required to test whether the mean number of units produced per week is the same for each assembly method in the Chemitech experiment. Suppose we introduce the following notation. (20 points)

And we want to use the sample means to test the following hypotheses.

The following steps are used to obtain the table.

Step 1. Click the **Data** tab on the Ribbon

Step 2. In the **Analysis** group, click **Data Analysis**

Step 3. Choose **Anova: Single Factor** from the list of Analysis Tools

Step 4. When the Anova: Single Factor dialog box appears:

Enter A1:C6 in **Input Range** box

Select **Columns**

Select **Labels in First Row**

Select **Output Range** and enter A8 in the box

Click **OK**

**Interpret the results (ANOVA table) using at least 50 words, providing discussions on whether mean number of units produced per week is statistically equal across three methods or not. **