The data below are weights of sample cereal bars in grams for two shift workers at an industrial plant. They used two different independent machines for their shifts to cut the cereal bars into shapes to a given mass. Assume that a statistical test found that the mass of cereal bars follow a normal distribution. Therefore, we will perform a z- test on this data, even though the sample sizes are less than 30.
To do this, you must enter the data into Excel in two columns. In the previous week I asked you to install MegaStat as add-in to your Excel, and I provided the instructions for doing so. You can simply copy and paste the data into Excel, and make sure all the numbers are lined up correctly.
|
Shift 1
|
Shift 2
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15
|
13.95
|
|
15
|
13.5
|
|
14.3
|
9
|
|
14.3
|
14.3
|
|
14.7
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14.4
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|
13.5
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15
|
|
14.3
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14.3
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|
14.9
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14.3
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|
14.3
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13.7
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|
15
|
14.3
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|
15
|
14.9
|
|
15
|
14.4
|
|
15
|
14.85
|
|
12.5
|
15
|
|
14.7
|
14.7
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|
15
|
12.75
|
|
15
|
14.25
|
|
12.75
|
13.5
|
|
14.25
|
13.5
|
|
14.25
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13.5
|
|
14.4
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13.25
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PROCEDURE:
From the Add-ins tab in Excel select MegaStat, then select Hypothesis tests, then select "Compare two independent groups." For Group 1, place the cursor into the space and go scroll from top to bottom the results for Shift 1 in the Excel column, including the heading. For Group 2, place the cursor in the space and go scroll from top to bottom the results for Shift 2 in the Excel column, including the heading. For hypothesized difference, select zero." For Alternative, select "greater than." Make sure that z-test is checked. Click OK.
Copy and paste your results into your response, and answer the questions below.
Questions:
(1) In this exercise how would you formulate the null and alternate hypothesis? Is this a one-tailed test, or a two-tailed test?
(2) Based on the output, can we conclude at the 5% level of significance that the machine used in shift 1 overcuts the cereal bars? How?