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(math144)[2003](f)midterm~mlfung^ans_10454.pdf
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Part A

1. (b) 2. (a) 3. (c) 4. (d) 5. (d)
6. (d) 7. (b) 8. (c) 9. (b) 10. (a)
11. (e) 12. (e) 13. (a) 14. (c) 15. (c)
16. (d) 17. (e) 18. (c) 19. (b) 20. (e)
21. (e) 22. (d) 23. (b) 24. (c) 25. (c)
26. (e) 27. (a) 28. (b) 29. (a) 30. (e)

Part B

1. (a) T , T , T , T , T






,








ANOVA table:

Source
SS
d. f.
MS
F-ratio

Angle
99.0236
4
24.7559
21.4

Error
23.1364
20
1.1568
/////////////////

Total
122.16
24
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(b) A 90% confidence interval for is given by








(c) From the data,
,
Y, ,



,




Regress Y on X,




Hence regression line of Y on X is given by : Y











ANOVA table:

Source
SS
d. f.
MS
F-ratio

Regression
97.2142
1
97.2142
89.6314

Error
24.9458
23
1.0846


Total
122.16
24





(d) At , point estimate of is




A 90% confidence interval for Y at is







(e) From the ANOVA tables, the proportion of variation explained by the ANOVA model is
while the proportion of variation explained by the simple linear regression model is
. Hence the ANOVA model can fit the data better than the simple linear regression model. This is expected as the linear regression model had implicitly assumed that the pressure is linearly related with the angles. The ANOVA model treats the five angles as nominal categories and didnt assume any linear relationship. Hence generally the ANOVA model can fit the data better than the simple linear regression model.

On the other hand, the imposed linearity assumption of the regression model can produce more informative result. This can be observed by the comparison of margin of errors in the estimations in part (b) and part (d). The confidence interval based on the regression analysis is slightly shorter than that based on the ANOVA model, indicating a more informative estimation.


2. (a) Assume normal populations, equal population variances and independent samples.

From the data,
, ,

, .

Pooled sample variance :


A 95% confidence interval for the effect of the supplement, , is





(b) A 95% confidence interval for the mean gain by applying the supplement is




Since all the values in this interval are less than $80, which is the cost of the supplement, it is not profitable to use it.

(c) Assuming equal sample sizes , equating the margin of error to 10 gives





Assuming large n and use the pooled sample standard deviation from the past data, we have



Hence two samples each of 77 steers will be needed.

3. (a) Let p the severe or fatal injury rate of occupant