Question

In a manufacturing process, the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data:

Line Speed	Number of Defective Parts Found
20	21
20	19
40	15
30	16
60	14
40	17

1) Use the data to develop an estimated regression equation that could be used to predict the number of defective parts found, given the line speed.

Select one:

a.

ŷ=-5x+120

b.

ŷ=101.34x+150.23

c.

ŷ=-0.1x+20.667

d.

ŷ=-0.148x+22.174

e.

ŷ=-3.988x+103.468

2)Test whether the regression parameters for the slope should be rejected at the 0.05 level of significance.

Select one:

a.

Reject null. The slope is equal to 0.

b.Reject null. The slope is not equal to 0.

c.

Accept the null. There is a relationship.

d.

Accept the null. There is not a relationship.

e.

Do not reject null. The slope is equal to 0.

3)

If the line speed was set to 50 ft/min, what would be your predicted number of defected parts?

Select one:

a.

14.784

b.

-95.952

c.

5.162

d.

15.667

e.

-130.000

4) Test whether the regression parameters for r should be rejected at the 0.05 level of significance.

Select one:

a.

Reject the null. There is not a relationship.

b.

Do not reject null. There is not a relationship.

c.

Reject the null. There is a relationship.

d.

Accept the null. There is a relationship.

e.

Accept the null. There is not a relationship.

5) Interpret your findings for the regression parameters, r and the slope, at the 0.05 level of significance.

Select one:

a.

Since the p values are much greater than the level of significance, in both cases, we confidently do not reject the null hypothesis that the data is not related, and that the slope is equal to 0.

b.

Since the p values are much less than the level of significance, we can confidently reject the null hypothesis that the data is not related, and the null hypothesis that the slope is equal to 0.

c.

Since the p values are much greater than the level of significance, inboth cases, we can confidently reject the null hypothesis that the data is not related, and that the slope is not equal to 0.

d.

Since the p values are much less than the level of significance, we confidently do not reject the null hypothesis that the data is not related, and that the slope is equal to 0.

6) How much of the variation in the number of defective parts found in the sample does the regression model you estimated explain? (Hint: Remember the statistic that you should use for this.)

Select one:

a.

0.860

b.

0.632

c.

0.180

d.

0.399

e.

0.739

Answer 1

We will run the regression analysis in excel

a)

2) The p-value for the test of the slope is 0.0281 which is less than the significance level 0.05.

Hence we will reject the null hypothesis.

option B is right

3) for X = 50

option is right

4)

option C is right

5) option B is right

6)coefficient of determination

which means that 0.739(or 73.91% ) of the variation in the number of defective parts found in the samplecan be explained by the regression model.

option e is right