SPSS Statistics: Correlation & Regression 'Data Analysis' Chapter

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Question 11D

1. What are the null and alternative hypotheses?

Null Hypothesis: Volume has no relation to defect rate (the slope is equal to 0).

Alternative Hypothesis: As volume increase, defect rate increases. (the slope is not equal to 0).

2. What is the population of interest? What is the sample?

All shifts at the plant in question make up the population of interest.

160 randomly selected shifts make up the sample.

3. On the basis of the output, what can you conclude about the null hypothesis?

The null hypothesis can be rejected. There is a significant linear regression between volume and defect rate and the slope is not equal to 0.

4. Can you reject the null hypothesis that the slope is 0?

Yes. The scatter plot shows a linear relationship and the regression coefficient is .740. The value of t is 13.846, indicating that the slope is 13.846 standard error units above a slope of 0, which has a significance of .000, therefore allowing one to reject the hypothesis that the slope is equal to 0.

5. Can you reject the null hypothesis that there is no linear relationship between the dependent and independent variables?

Yes. There is a relationship between the dependent and independent variables, as evidenced by the significant regression analysis and the significant correlation coefficient.
6. Can you reject the null hypothesis that the population correlation coefficient is 0?

Yes, when we reject the null hypothesis that the slope is equal to 0, this allows us to also reject the null hypothesis that the population correlation coefficient is equal to 0.

7. What would you predict the defect rate to be on a day when the volume is 4200 units? What would you predict the average defect rate to be for all days with production volumes of 4200?

Predicted Defect Rate = 0.027 (4200) -- 97.073

= 16.327

The average defect rate for all days with production volumes of 4200 would also be 16.327.

8. In what way do the two estimates of the defect rate in the question above differ?

The predicted values are the same, but the variability would be different.

Question 11E

1a.

Father's education = .760(mother's education) + 2.572

1b.

Yes, the null hypothesis can be rejected. There is a linear relationship between father's and mother's education.

1c.

40.8% of the variability in father's education can be explained by mother's education.

1d.

If the slope value is positive, we know that as the value of one variable increases the value of the other variable.....

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