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# Hypothesis testing for relationship between defect and volum

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3. You obtain the following regression statistics for the relationship between defect and volume at one of your plants. You have a random sample of results from 160 shifts at the plant.

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimated
1 .740 .548 .545 4.92

Model Sum of Squares df Mean Square F Sig.
1 Regression 4647.124 1 4647.124 191.717 .000
Residual 3829.839 158 24.239
Total 8476.963 159

Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) -97.073 7.819 50.995 .000
VOLUME .027 .002 .740 13.846 .000

QUESTIONS;
a) What are the null and alternative hypothesis?
b) What is the population of interest? What is the sample?
c) On the basis of the output, what can you conclude about the null hypothesis?
d) Can you reject the null hypothesis that the slope is 0?
e) Can you reject the null hypothesis that there is no linear relationship between the dependent and independent variable?
f) Can you reject the null hypothesis that the population correlation coefficient is 0?
g) 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?
h) In what way do the two estimates of the defect rate in question 3g differ? Calculations not required.