Applied Statistics Practice Exercise

· Questions 11.6

Use the output Minitab for these data to answer the following questions.

x	y
20	32
36	75
50	87
80	152
95	195
121	274
85	184
63	123
98	136
108	203

a. Plot the data on a spreadsheet.

b. Locate the least-squares prediction from the output given here, and draw the regression line in the scatterplot

c. Does the predicted equation seem to represent the data adequately?

d. Predict y when x=77

· Questions 11.8

An online retailer needs to manage the amount of time needed to select the ordered items and assemble them for shipping. In order to assess the amount of time his assemblers devote to this task, the retailer takes a random sample of 100 orders and records the number of items in each order (Noltems) and the time needed to assemble the shipment.

NoItems	Time
1	4.8
1	14.7
1	13.7
1	9.5
1	2.4
1	11.8
2	10.5
2	12.0
2	14.3
2	16.4
2	17.9
3	14.5
3	16.7
3	20.1
3	16.8
3	20.8
3	26.8
3	12.9
3	13.0
3	15.4
4	10.8
4	20.3
4	22.3
4	20.0
4	21.9
4	20.7
4	20.9
4	19.9
4	17.1
5	19.1
5	17.2
5	18.1
5	17.9
5	12.9
6	19.6
6	27.9
6	22.2
6	23.2
6	17.5
6	15.3
6	21.8
7	17.9
7	20.1
7	18.9
7	29.3
7	21.5
8	26.5
8	28.2
8	25.1
8	26.1
8	28.2
8	22.3
9	21.8
9	25.5
9	24.4
9	18.1
9	26.7
10	24.6
10	30.1
10	21.5
10	25.2
10	28.2
10	22.6
11	31.3
11	27.2
11	28.8
11	29.7
12	34.3
12	27.9
12	29.7
12	28.7
14	34.6
14	38.0
15	28.0
16	37.0
17	32.5
18	39.5
18	39.0
18	37.0
19	35.5
20	38.3
21	44.0
22	39.6
23	42.3
24	34.6
25	44.9
25	47.4
25	49.2
26	45.8
27	44.0
27	46.1
30	42.9
30	48.3
31	46.0
37	48.2
39	54.7
40	49.9
41	55.4
45	57.1
46	52.4

a. Plot the data on a scatterplot

b. Fit a least-squares line to the data, and comment on the degree of fit to the data

c. Fit a regression model with the square root of Noltems as the explanatory variable

d. Which model produced a better fit to the data?

e. Predict the amount of time needed to assemble a package containing 13 items using both models. Was there much difference in your predictions?

· Questions 11.22

Athletes are constantly seeking measures of the degree of their cardiovascular fitness prior to major race. Athletes want to know when their training is at a level which will produce a peak performance. One such measure of fitness is the time to exhaustion from running on a treadmill at a specified angle and speed. The important question is then “Does this measure of cardiovascular fitness translate into performance in a 10km running race?” 20 experienced distance runners who professed to be at top condition were evaluated on the treadmill and then had their times recorded in a 10km race. The data are given here:

Treadmill	10-K
7.5	43.5
7.8	45.2
7.9	44.9
8.1	41.1
8.3	43.8
8.7	44.4
8.9	42.7
9.2	43.1
9.4	41.8
9.8	43.7
10.1	39.5
10.3	38.2
10.5	43.9
10.7	37.1
10.8	37.7
10.9	39.2
11.2	35.7
11.5	37.2
11.7	34.8
11.8	38.5

a. Plot the data on a scatterplot

b. Fit a least-squares line to the data. Does a linear model seem appropriate?

c. Obtain the estimated linear regression model = +

Questions 11.27

A firm that prints automobile bumper stickers conducts a study to investigate the relation between the direct cost of producing an order of bumper stickers (TOTCOST) and the number of stickers (RunSize, in 1,000s of stickers) in a particular order. The data are given in the following table.

Runsize	TOTCOST
2.6	230
5.0	341
10.0	629
2.0	187
0.8	159
4.0	327
2.5	206
0.6	124
0.8	155
1.0	147
2.0	209
3.0	247
0.4	133
0.5	125
5.0	366
20.0	1146
5.0	339
2.0	208
1.0	150
1.5	179
0.5	128
1.0	155
1.0	143
0.6	131
2.0	219
1.5	171
3.0	258
6.5	415
2.2	226
1.0	159

a. Plot a scatterplot of the data. Do you detect any difficulties with using a linear regression model? Can you find any blatant violations of the regressions assumptions?

b. Compute the estimated regression line

c. Estimate the residual standard deviation

d. Construct a 95% confidence interval for the trust slope

e. What are the interpretations of the intercept and slope in this study?

· Questions 11.32

A chemist is interested in determining the weight loss (y) of a particular compound as a function of the amount of time the compound is exposed to the air. The data in the following table give the weight losses associated with n=12 settings of the independent variable, exposure time.

WeightLoss	ExposureTime
4.3	4
5.5	5
6.8	6
8.0	7
4.0	4
5.2	5
6.6	6
7.5	7
2.0	4
4.0	5
5.7	6
6.5	1

a. Determine the least-squares prediction equation for the model

= + X +

b. Test : 0; give the p-value for ≥, and draw conclusions

· Questions 11.38

A manufacturer of laundry detergent was interested in testing a new product prior to market release. One area of concern was the relationship between the height of the detergent suds in a washing machine as a function of the amount of detergent added in the wash cycle. For a standard size washing machine tub filled to the full level, the manufacturer made random assignments of amounts of detergent and tested them on the washing machine. The data appear next.

Amount	Height
6	28.1
6	27.6
7	32.3
7	33.2
8	34.8
8	35.0
9	38.2
9	39.4
10	43.5
10	46.8

a. Plot the data

b. Fit a linear regression model

c. Use a residual plot to investigate possible lack of fit

· Questions 11.44

A survey of MBA, graduates of a business school obtained data on the first-year salary after graduation and years of work experience prior to obtaining their MBA. The data are given in the following table with salary in thousands of dollars.

EXPER	SALARY
8	113.9
5	112.5
5	109.0
11	125.1
4	111.6
3	112.7
3	104.5
3	100.1
0	101.1
13	126.9
14	97.9
10	113.5
2	98.3
2	97.2
5	111.3
13	124.7
1	105.3
5	107.0
1	103.8
5	107.4
5	100.2
7	112.8
4	100.7
3	107.3
3	103.7
7	121.8
7	111.7
9	116.2
6	108.9
6	111.9
4	96.1
6	113.5
5	110.4
1	98.7
13	120.1
1	98.9
6	108.4
2	110.6
4	101.8
1	104.4
5	106.6
1	103.9
4	105.0
1	97.9
2	104.6
7	106.9
5	107.6
1	103.2
1	101.6
0	99.2
1	101.7
6	120.1

a. Plot the data in a scatterplot. Based on the plotted data, does it appear that those students having less experience also have similar salaries?

b. Identify any student who do not seem to satisfy the pattern or larger salaries associated with more experiences

· Questions 11.50

There has been an increasing emphasis in recent years on making sure that young women are given the same opportunities to develop their mathematical skills as young men are given in U.S educational system. The following table provides the SAT scores for male and female students over a 34 year period.

Gender/Type	Male/Verbal	Female/Verbal	Male/Math	Female/Math
1980	506	498	515	473
1981	508	496	516	473
1982	509	499	516	473
1983	508	498	516	474
1984	511	498	518	478
1985	514	503	522	480
1986	515	504	523	479
1987	512	502	523	481
1988	512	499	521	483
1989	510	498	523	482
1990	505	496	521	483
1991	503	495	520	482
1992	504	496	521	484
1993	504	497	524	484
1994	501	497	523	487
1995	505	502	525	490
1996	507	503	527	492
1997	507	503	530	494
1998	509	502	531	496
1999	509	502	531	495
2000	507	504	533	498
2001	509	502	533	498
2002	507	502	534	500
2003	512	503	537	503
2004	512	504	537	501
2005	513	505	538	504
2006	505	502	536	502
2007	503	500	532	499
2008	502	499	532	499
2009	502	497	533	498
2010	502	498	533	499
2011	500	495	531	500
2012	498	493	532	499
2013	499	494	531	499

a. Plot the six pairs of data values in scatterplots. Male/Verbal versus Female/Verbal, Male/Math versus Male/Verbal, and so on.

b. Which, if any, of the six correlations are significantly different from 0 at the 5% level?

c. Do the plots reflect the sizes of the correlations between the pairs of variables?

d. Are male verbal scores more correlated with male and female math scores?