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CHAPTER 3: Solutions to Selected Exercises

3.1 a. Scatterplot of Salary vs GPA

[pic]

b. The straight line appearance of the plot in Part a indicates that a simple linear regression model should be appropriate.

3.2 a. [pic] is the mean of the population of all potential starting salaries for marketing graduates having a 4.00 GPA.

b. [pic]is the mean of the population of all potential starting salaries

for marketing graduates having a 2.50 GPA.

c. [pic]= the change in mean starting salary associated with a one point increase in the grade point average.

d. [pic]= the mean starting salary for marketing graduates with a grade point average of 0.00.

The interpretation of [pic]fails to make practical sense because it requires that a marketing graduate have a grade point average of 0.00.

e. All factors other than the grade point average. For example, extra-curricular activities and overall GPA.

3.3 a. [pic]=5.70657 may be interpreted as follows:

An increase of one point in the GPA corresponds to an increase of $5,706.57 in the average starting salary.

[pic] clearly has no practical interpretation because it indicates a mean starting salary of $14,815.60 when the GPA=0.000.

b. [pic] ($33,362)

c.

[pic]

[pic]

Note: For more accurate estimate carry more decimal places.

3.4 a. [pic]

[pic]

b. [pic]

[pic]

Note: For more accurate estimate carrying more decimal places, starting in Exercise

3.3. Round-off-error can be surprisingly large.

5. The straight line appearance of the data plot indicates that a simple linear regression model should be appropriate.

6. a. It is the mean of the service times required when the number of copiers is 4.

b. It is the mean of the service times required when the number of copiers is 6.

c. The slope parameter equals the change in the mean service time that is associated with each additional copier serviced.

d. The intercept is the mean service time when there are no copiers. It could make practical sense if it requires service time to be 0 when no copies are serviced.

e. All factors other than the number of copiers serviced.

3.7 a. [pic] may be interpreted as follows: An increase of one copier serviced corresponds to an increase of 24.6 minutes in the mean time required.

[pic]clearly has no practical meaning because it indicates that the mean service time is 11.464 minutes for 0 copiers.

b. [pic] (109.9 minutes)

c.

. [pic]

[pic]

[pic]

3.8 a. [pic]

[pic]

b. [pic]

[pic]

9. A straight line appears to be a reasonable approximation for relating the average demand to price difference.

10. a. Mean demand when price difference is .10.

b. Mean demand when price difference is -.05.

c. Change in mean demand per dollar increase in price difference.

d. Mean demand when price difference = 0; yes

e. Factors other than price difference, such as amount and type of advertising.

3.11 a. [pic] has the following interpretation:

For each increase in the price difference (fresh price - ind. price) of one dollar, the mean demand for Fresh increases by 266, 522 bottles.

[pic] has the following interpretation:

When there is no price difference between fresh price and average industry price, mean demand for the large bottle of Fresh is 781,409 bottles.

b. [pic]

c. [pic]

8.5 = 7.81409 + 2.6652x

[pic]or about 26 cents

d. [pic]

[pic]

12. a.

[pic]

b. Since the relationship between direct labor cost (y) and batch size (x) has a straight appearance, a simple linear regression model is appropriate.

3.13 a. Mean labor cost when batch size = 60.

b. Mean labor cost when batch size = 30.

c. Change in mean labor cost per unit increase in batch size.

d. Mean labor cost when batch size = 0. This could make sense if mean labor cost is 0 when batch size is 0.

e. Factors other than batch size; answers will vary.

3.14 a.

[pic]

[pic]

b. [pic]is the estimated increase in mean labor cost ($1014.63) for every 1 unit increase in the batch size.

[pic]is the estimated mean labor cost (18.4880) when batch size = 0; no.

c. [pic]

d. [pic]

3.15 a. [pic] [pic]

b. [pic]

= 3,811,300 [pic][(18.48751)(5,782)+(10.14626)(365,027)]

= 746 (Carry more decimal places in 3.14 Part a for more accuracy)

3.16 a. [pic]=14.816 [pic]=5.7066

b. SSE = 1.438 [pic] s=.536321

c. [pic] t = 14.44

[pic]

d. [pic] Reject [pic], strong evidence of a significant linear relationship between x and y.

e. [pic] Reject [pic], very strong evidence of a significant linear relationship between x and y.

f. p-value = .000 Reject at all [pic], extremely strong evidence of a significant linear relationship between x and y.

g. 95% [pic]

We are 95% confident that the mean starting salary increases by between $4690 and $6723 for each 1.0 increase in GPA.

h. 99% [pic]

We are 99% confident that the mean starting salary increases by between $4113 and $7300 for each 1.0 increase in GPA.

i. [pic]

[pic]

j. p-value = .000 Reject at all [pic], Extremely strong evidence that the y-intercept is significant.

k. [pic]

[pic]

3.17 a. [pic]

b. [pic]

c. [pic]

[pic]

d. [pic] Reject [pic], strong evidence of a linear relationship between [pic].

e. [pic] Reject [pic], very strong evidence of a linear relationship between [pic].

f. p-value = .000 Reject at all [pic], extremely strong evidence of a linear relationship between [pic].

g. [pic]

h. [pic]

i. [pic]

[pic]

j. p-value = .0087 Reject at all [pic]except .001, very strong evidence of a linear relationship between [pic].

k. [pic]

[pic]

3.18 a. [pic]

b. [pic]

c. [pic] [pic]

d. [pic] Reject [pic], strong evidence of a linear relationship

e. [pic] Reject [pic], very strong evidence of a linear relationship

f. p-value = 0.000 < .001. Reject [pic], extremely strong evidence of linear relationship.

g. [pic]

h. [pic]

i. [pic]

j. p-value = 0.000 < .001; reject [pic].

k. [pic]

[pic]

3.19 a. [pic]

b. [pic]

c. [pic] [pic]

d. [pic] Reject [pic], strong evidence of a linear relationship

e. [pic] Reject [pic], very strong evidence of a linear relationship

f. p-value = 0.000; Reject [pic]at each value of [pic], extremely strong evidence of linear relationship.

g. [pic]

h. [pic]

i. [pic]

j. p-value = 0.003; fail to reject[pic]at [pic]= .001. Reject [pic]at all other values of [pic].

k. [pic]

[pic]

3.20 a. 33.362, [32.813, 33.910]

b. 33.362, [31.878, 34.846]

c. Distance Value =[pic]

[pic]

[pic]

3.21 a. 109.873, [106.7207, 113.0252]

b. 109.873, [98.9671, 120.7788]

c. 113 minutes

3.22 a. 8.0806, [7.9479, 8.2133]

b. 8.0806, [7.4187, 8.7425]

c. See graph with Exercise 3.22. A vertical line at Pricedif = 0.1 will cross the curves at the points that correspond to the values for 95% CI (Part a) and 95% PI (Part b).

d. [pic]

[pic]

[pic]

e. a) 8.4804, [8.3604, 8.6004]

b) 8.4804, [7.8209, 9.1398]

c) Use vertical line at Pricedif = .25

d) [pic]

[pic]

3.23 a. 627.2630, [621.0544, 633.4717]

b. 627.2630, [607.0322, 647.4939]

c. [pic]

[pic]

3.24 a. 61.380; 1.438; 59.942; [pic]=.977, r =.988

97% of the total variation in the starting salaries can be explained by the linear relationship between the starting salaries and GPA.

b. [pic] (Difference from 14.44 is round-off error. Need [pic]with more decimal places.)

Since [pic]

we can reject [pic]at [pic]=.05 and [pic]=.01

3.25 a. 20,111; 191.70166; 19,919; [pic]=.9905, r = .9952

99.05% the total variation in service time can be explained by the linear relationship between service time and the number of copiers serviced.

b. [pic] (Difference from 30.58 is round-off error)

[pic]

Reject [pic]: [pic]=0 at [pic]=.05 and [pic]=.01

3.26 a. 13.459; 2.806; 10.653; .792; .890

79.2% of the total variation in demand can be explained by the linear relationship between demand and price difference.

b. [pic] (Difference from 10.31 is round-off error)

[pic]

3.27 a. 1,025,340; 746.76238; 1,024,593; .9993; .9996

99.96% of the total variation in direct labor costs are explained by the linear relationship between direct labor costs and batch size.

b. [pic] (Difference from 117.13 is round-off error)

[pic]

Reject [pic]at [pic]=.05 and [pic]=.01.

3.28 a. F = 59.942 /(1.438 / 5) = 208.42 (approximately 208.39, round-off error)

b. [pic]

Since 208.39 > 6.61, reject [pic]with strong evidence of a linear relationship between x and y.

c. [pic] [pic]

Since 208.39 > 16.26, reject [pic] with very strong evidence of a significant relationship between x and y.

d. p-value = .000; Reject [pic]at all levels of [pic], extremely strong evidence of a significant relationship between x and y.

e. [pic] (approximately equals F = 208.39, round-off error)

f. [pic]

3.29 a. F =19919 / (191.70166/9) = 935.16 (approximately 935.15, round-off error)

b. [pic][pic]

Since 935.15 > 5.12, reject [pic]with strong evidence of a linear relationship between x and y.

c. [pic] [pic]

Since 935.149 > 10.56, reject [pic]with very strong evidence of a linear relationship between x and y.

d. p-value = less than .001; Reject [pic]at all levels of [pic], extremely strong evidence of a linear relationship between x and y.

e. [pic] (approximately equals F = 935.15)

[pic]

3.30 a. F = 10.653 / (2.806 / 28) = 106.30

b. [pic], reject [pic][pic]. Strong evidence of a linear relationship between x and y.

c. [pic], reject [pic][pic]. Very strong evidence of a linear relationship between x and y.

d. p-value = .000 and is less than .001, reject [pic]. Extremely strong evidence of a linear relationship between x and y.

e. [pic]

[pic]

3.31 a. F = 13,720.5

b. [pic] [pic]

Since 13,720.5 > 4.95, reject [pic]at [pic]

c. [pic] [pic]

Since 13,720.5 > 10.04, reject [pic]at [pic]= .01

d. p-value = .000; reject [pic] because .000 < .001, extremely strong evidence of a linear relationship.

e. (117.13)[pic]=13,719.4 (approximately equals 13,720.5, round-off error)

[pic]

3.32 a. Using Figure 3.21, there does seem to be a negative relationship between temperature and o-ring failure.

b. The temperature of 31[pic]was outside the experimental region.

3.33 a. Yes, diet and type of exercise. While this evidence definitely indicates a potential link between smoking and lung cancer, a well-designed study will take into account other factors.

b. The two slopes appear to differ. A statistical test is needed to show if there is in fact a statistical difference. It appears that the incidence of lung cancer increases more rapidly when one increases amount of smoking at low levels of smoking than when a heavy smoker does a similar increase.

3.34 a. Yes, there is a linear relationship at [pic] because the p-value for [pic] vs. [pic] is .000196916. There is extremely strong statistical evidence.

b. [pic]

95% C.I. for [pic]is [19.2, 51.3]

Thus, we are 95% confident that a 1% increase in the percentage of minority population corresponds to an increase of between 19 and 51 in the mean number of residents per branch bank.

3.35 [pic]

3.36 Minitab Output

[pic]

a. When x = 15, [pic]

And 95% C. I. for mean market return rate is [8.494, 11.514]

b. When x = 15, [pic]and 95% P. I. for market return rate of this individual stock is [-0.310, 20.318]

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