Question

In: Statistics and Probability

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The labor quotation department at Excabar, a large manufacturing company, wants to verify the accuracy of their labor bidding process (estimated cost per unit versus actual cost per unit). They have randomly chosen 35 product quotations that subsequently were successful (meaning the company won the contract for the product). The data is presented to the left of this text.




1. Set up the hypotheses to test whether the Estimated cost/unit is significantly different than the Actual cost/unit.

2. Using the appropriate commands in Excel, find the value of the test statistic. Assume the populations variances are unknown but equal. Compute the 99% Confidence Interval for each variable.


3. Interpret the p- value at α = .01

4. Based on these results, write a statement expressing the results of this study.

Null:   μ      μ
Alternative:   μ      μ

Product   Estimated cost/unit   Actual cost/unit
1   13.90   12.90
2   18.80   15.80
3   14.80   11.80
4   11.80   11.80
5   16.80   12.80
6   14.20   13.20
7   21.80   18.80
8   6.80   10.80
9   19.50   18.50
10   21.00   19.00
11   12.40   11.40
12   15.10   18.10
13   15.80   15.80
14   24.90   23.90
15   13.20   16.20
16   25.90   23.90
17   12.80   10.80
18   12.90   11.90
19   20.50   19.50
20   19.00   18.00
21   10.80   10.80
22   10.80   13.80
23   18.80   17.80
24   12.60   11.60
25   26.80   22.80
26   22.90   24.90
27   22.80   19.80
28   12.50   16.50
29   15.50   15.50
30   14.10   13.10
31   15.10   19.10
32   12.50   10.50
33   21.90   22.90
34   24.20   20.20
35   17.80   14.80

Expert Solution

1) The null and alternative hypotheses are defined as,

There is no difference in estimated cost per unit versus actual cost per unit

There is a significant difference in estimated cost per unit and actual cost per unit

2) The t statistic for the dependent samples t test is obtained using the formula,

Where, the difference is

obtained in excel. The screenshot is shown below,

The average of difference is obtained in Excel. The screenshot is shown below,

The standard deviation of difference is obtained in Excel. The screenshot is shown below,

The t statistic is calculated using the formula described above. The screenshot is shown below,

Confidence Interval

The 99% confidence interval for each variable is obtained in excel using the formula,

The screenshot are shown below,

3)

The p-value for the t test is obtained in excel. The screenshot is shown below,

4)

Since the P-value = 0.1213 is greater than 0.01 at 1% significance level, the null hypothesis is rejected. It can be stated now, there is no difference in estimated cost per unit and actual cost per unit

orchestra answered 1 year ago

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