ES8 Exercises for Web Posting - Solutions

ES9 Additional Exercises - Answers Chapter 1

1. a. inferential b. descriptive

2. a. judgment sample b. No, not a probability sample.

3. a. All Alzheimer patients in the U.S. b. Cost in medical expenses and lost productivity per patient per year. c. Total cost per year for all Alzheimer patients in the U.S. d. Total cost per year for the Alzheimer patients used as a sample.

4. qualitative

5. a. Attribute data b. Judgment sample, most likely. Chapter 2

1. HOW TO SAY I LOVE YOU

100 100

80 t t 60 n n e u c

50 r o e C

ss g ft nd Ki ilin gi ha er Affection g- m ive ld th Hu S G Ho O Count 51 20 10 10 9 Percent 51.0 20.0 10.0 10.0 9.0 Cum % 51.0 71.0 81.0 91.0 100.0

2. a. Types of Waste in US Landfills

100 100

80 t t 60 n n e u c

50 r o e C

te r ic l r as d s pe st ta he w oo s Waste pa la me ot rd f gla p ya Count 38 18 14 13 11 4 2 Percent 38.0 18.0 14.0 13.0 11.0 4.0 2.0 Cum % 38.0 56.0 70.0 83.0 94.0 98.0 100.0

b. "Other" in middle is inconsistent with Pareto format. Need more information on unclassified data. 3. a. Stem-and-Leaf: 50 Common Stocks 1 1 7 9 7 6 3 3 7 2 7 1 2 4 2 6 8 6 6 2 4 2 1 8 5 7 3 0 5 1 1 7 6 5 8 2 4 1 7 5 8 3 5 8 2 2 4 2 7 2 6 5 7 2 5 5 8 9 0

b. Lowest price - $11, highest price - $90. c. More between $10 and $20 than in any other interval.

4. a. “size”; Number of Children Living at Home. “frequency”; Number of Mexican-American Women.

Mexican-American Women

20 17 y c n e u

q 10 e r 7 F

0 1 2 3 4 No. Children 5. a. Third-graders at Roth Elementary School : . . : . : . . : . : : : . . . . : : : : : . : : . : . : : : : : : : : : . : +------+------+------+------+------+-ST 0.0 5.0 10.0 15.0 20.0 25.0

Third Graders Physical Strength Test

10 y c n e

u 5 q e r F

1 4 7 10 13 16 19 22 25 PhyStren

10 y c n e

u 5 q e r F

0 3 6 9 12 15 18 21 24 27 PhyStren d.

c 10 n e u q e r

-2.5 2.5 7.5 12.5 17.5 22.5 27.5 PhyStren

f. Seems to be bimodal distribution.

6. a. Class limits frequency relative frequency 2.00 - 3.00 4 0.100 3.00 - 4.00 13 0.325 4.00 - 5.00 12 0.300 5.00 - 6.00 8 0.200 6.00 - 7.00 2 0.050 7.00 - 8.00 1 0.025 40 1.000

Quik Delivery Fees

t 20 n e c r e P 10

1 2 3 4 5 6 7 8 fees 7. åx = 36709 a. x = 2622 b. d(x ) = 7.5th; x = $2494 c. $2998.50 d. no mode

8. a. x = 5255/27 = 194.6 d(x ) = 14th; x = 190

b. Stem-and-leaf of SchoolYr N = 27 Leaf Unit = 1.0 1 16 0 2 17 5 11 18 000024555 (7) 19 0001225 9 20 000 6 21 166 3 22 0 2 23 3 1 24 3

c. Mean is arithmetic average, median is middle value. The two high numbers increase the mean.

9. a. midrange = 54.75 b. Highest and lowest values were the only data given. c. The distribution of state average greens’ fees must be skewed to the right.

10. a. midrange = 25,891 b. The distribution of the 50 state averages must be slightly skewed to the left since the average is slightly larger than the midrange.

11. n = 14, åx = 36,709, åx² = 103,772,173 a. 578,350.2 b. 760.5

12. a. range = 83 n = 27, åx = 5,255, åx² = 1,031,585 s = 18.4 b. 1 16 0 2 ½ 17 5 11 ½ 18 000024555 (7) ½ 19 0001225 9 ½ 20 000 6 ½ 21 166 3 ½ 22 0 2 ½ 23 3 1 ¯ 24 3

c. mounded, slightly skewed

13. n = 123, åxf = 3,387,312, åx²f = 93,827,350,800 a. $3,387,312 b. $27,539 c. Academic d. $2111

14. a. nk/100 = 10.0; d(P25) = 10.5th Q1 = 8.3 b. nk/100 = 20.0; d(P50) = 20.5th Q2 = 9.25 c. nk/100 = 30.0; d(P75) = 30.5th Q3 = 10.85 d. nk/100 = 38.0; d(P95) = 38.5th P95 = 14.8 e. 7.1, 8.3, 9.25, 10.85, 15.5 f.

Manual Dexterity Study

16 15 14 13 e

m 12 i T

k 11 s a

T 10 9 8 7 15. a. d(x ) = 18th; x = 33.0 b. 34.8

c. nk/100 = 8.75; d(P25) = 9th Q1 = 31.3

nk/100 = 26.25; d(P75) = 27th Q3 = 36.0 midquartile = 33.65

d. 30.1, 31.3, 33.0, 36.0, 39.5

Ignition Times

40 39 38 37 36 e m i 35 T n

g 34 I 33 32 31 30

16. -0.86, 1.68

17. a. 9.10 to 37.18 b. » 84%

18. n = 50, x = 787.00, x2 = 21027 a. Dotplot:

One-way Commute : : :. : . : . . :::: ..: :.::. : ::.. :: . .. . +------+------+------+------+------+------Time 0 12 24 36 48 60 Histogram:

One-way Commute

10 y c n e u q e r

0 10 20 30 40 50 60 70 Time (min.)

Boxplot:

One-way Commute

0 10 20 30 40 50 60 70 Time (min.)

b. Mean: 15.74 Median: d( x~ ) = 25.5th; x~ = 13.50 Mode: 3 Midrange: 32.5 Midquartile: 5, 22; 13.5

c. s2 = 176.319, s = 13.28, Range = 63

19. n = 20, åx = 93.6, åx² = 541.56; 4.68, 2.33; 0.02 to 9.34; 95% (19 of the 20) 20. Each student will have a different sample.

21. a.

Children Living at Home

40 38 Mex-Am erican Anglo-Am erican

n 30 e m o 23 22 W

f 20 o

17 r 15 e b m

u 10 9 9

1 1 0 0 1 2 3 4 Number of Children

b. n = åf = 70, åxf = 81, åx²f = 169; 1.2, 1.0 c. n = åf = 72, åxf = 70, åx²f = 166; 1.0, 1.2 d. Yes.

22. b. 4.6, 13.75, 22.65, 30.10, 41.1 c. 21.925, 16.35 d. 1.89, -1.52, 0.40 e. No. Chapter 3

Children's Fear of Hospitals

35 S F M C 30

8 9 10 11 Age

Walter's Payton's Rushing Records

1500 s

d 1300 Y l a t 1100 o T 900

500 200 300 400 n(carry)

b. Two separate groups of data points. c. First year and last year of his career, and probably a year when a serious injury restricted his playing time. 3. a. Scatter diagram:

Total Solar Eclipses

300 ) s (

t 200 a r u D 100

0 100 200 300 400 Width (mi)

4. åx = 96, åy = 309, åx² = 932, åxy = 2973, åy² = 9787 a. 10.4 b. 238.9 c. 6.6 d. 0.13

5. åx = 34.1, åy = 339, åx² = 123.73, åxy = 1076.9, åy² = 12,405 a. 7.449 b. 912.9 c. -79.09 d. -0.96

6. a. åx = 161, åy = 201, åx² = 4065, åxy = 4321, åy² = 6275 r = -0.707 b. If a person does not enjoy his job, he is more likely to be looking for another job. 7. a.

Cable Television Video Networks

r 66 e b i r c s b u

5000 15000 25000 Affiliates

b. åx = 200464, åy = 1193.0, åx² = 2689703492, åxy = 13479155, åy² = 79392 r = 0.5025; positive correlation.

8. a. åx = 52,750, åy = 639,272, åx² = 895,218,750, åxy = 8,072,375,500, åy² = 82,434,334,112

r = 0.986

b. As the enrollment increased so did the space available for recreation increase.

9. 1.1583

10. 2.75 11. a.

A Multistate Analysis of Active Life Expectancy

16 r Y n i

a 11 m e R

65 75 85 Age

b. åx = 740, åy = 109.9, åx² = 55090, åxy = 7947.9

y = 52.4 - 0.56x

c. Points (64,16.6) and (80,7.6) are used to locate the line.

d. approximately 13

e. No, one's age and years remaining should total a fixed value, life expectancy.

12. a.

Cash Registers

200 t s o C n

i 150 a M

0 1 2 3 4 5 6 7 8 9 Age

b. åx = 72, åy = 2163, åx² = 476, åxy = 12,677

y = 78.95 + 14.69x c. $196.47 d. The expected average cost of maintenance for all 8-year-old cash registers.

13. a.

Foreign Cars

50 y , e c i r

2 3 4 5 6 7 8 Age,x

b. n = 19, åx = 95, åy = 859, åx² = 529, åxy = 3849

y = 86.51 - 8.26x

c. Points (3,62) and (7,29) are used. d. 45.21 ($100)

14. åx = 106, åy = 332, åx² = 1438, åxy = 4446, åy² = 14,024

a. 0.518 b. y = 22.9 + 1.403x 15. a. Each person will have a different answer. b.

Balancing Work and Play

50 Work Play

40 s r u o

1975 1985 1995 Year

c. Yes, as work hours increase, leisure hours decrease slightly.

Balancing Work and Play

21.5 e r

u 20.5 s i e

L 19.5

43 44 45 46 47 48 49 50 51 Work

The scatter diagram seems to suggest that an increase in number of work hours is related to fewer hours of leisure. 16. a.

Fast-food

a 30 F

0 100 200 300 400 500 600 700 800 900 Calories

n = 18, åx = 7055, åy = 367, åx² = 3,287,783, åxy = 164,625, åy² = 10,309

b. 0.541 c. y = 4.80 + 0.04x d. If the calories increase so does the fat content.

17. a.

Blacknose Dace Minnow

100 90 80

70 h t g

n 60 e l 50 40

30 20 10 0 1 2 3 4 age

n = 10, åx = 19, åy = 491, åx² = 49, åxy = 1196, åy² = 30,221

b. 0.937 c. y = 10.34 + 20.40x d. If the age increases so does the length. 18. a. Scatter diagram:

Scatter Diagram of 5-Year Total Return and Risk Assessment

n 40 r u t

e 30 R

l ) a t % 20 ( o T

r 10 a e Y - 0 5 0 5 10 15 20 25 Risk Assessment

b. r = .8388 c. Yes. Chapter 4

1. a. No. b. Yes. c. 26/44 d. 38/44

2. (6.29908  10 –12 )(1.53908  10 –6) = 9.69479  10 –18 Agree.

3. a. 0.5041 b. 0.0841 c. 0.357911

4. 0.054872

5. a. 0.5375 b. 0.175 c. 0.6125

6. a. 0.71429 b. 0.66667 c. 1.00000

7. a. 0.9

b. P(D|C) = 1/4 = 0.25; P( D |C) = 1 - 1/4 = 3/4;

P(C and D ) = 0.075

c. P(C and D) = 0.025

8. c. The fewest,1290 is 1290 out of 13380 or 0.0964; while the most, 1383 is 1383 out of 13380 or 0.10336. These extremes seem very close to the expected 10%.

9. 0.28 Chapter 5

1. a. how women define holiday shopping: "a pleasure", "a chore", "no big deal", or "a nightmare". b. attribute, not a numerical variable.

2. No.

3. a. 2.44, 0.73 b. Calculated mean and standard deviation are smaller than true values.

4. b. 3.0 e. Mean of squared deviation = 1.0 f. Variance is the mean of the squared deviations.

5. 0.196

6. 0.668

7. 0.889

8. 0.051

9. a. 0.463 b. 0.537

10. a. 0.006 b. 0.121 c. 0.167 d. 0.367

11. a. 0.4400 b. 0.0507 c. 0.0048 20 x 20x 12. P(x)   0.48 (0.52) ; x  0,1,...,20  x 

a. 0.0313 b. P(x ³ 3) = 0.9996

5 x 5-x 13. a. P(x) =   (0.75) (0.25) for x = 0, 1, ... , 5 x

0.2 ) x ( P

0 1 2 3 4 5 x

c. 3.75, 0.97

14. Minority Group Mean, np Standard Deviation, npq Asian 1.50 1.187 Black 6.05 2.141 Hispanic 4.90 1.985

15. a. 0.070

b. One trial = one person, n = 10, success = "alone", failure = "other than alone", p = P(alone) = 0.48, q = 0.52, x = n(alone) = 0,1,...,10. 16. a. p3 + 3p2q

b. 0.028

c. 0.896

d. when p is greater than 0.5

e. 0, 0.5, or 1.0

17. a. p2 + pq

b. 0.100

c. 0.800

d. The probability that the committee makes the right decision is the same as the manager making the right decision, assuming the manager is not the one rolling the die.

e. p can be any number 0 £ p £ 1.

f. The third member makes the decision by rolling the die. Chapter 6

1. a. 0.6826 b. 0.9544 c. 0.9974 d. 0.6826 » 68%; 0.9544 » 95%; 0.9974 » 99.7%

2. a. 0.0038 = 0.38% b. 0.00003 (practically zero)

3. 0.0301

4. a. 0.1131 b. 0.0505 c. 4.64 minutes

5. a. 0.0401 = 4% b. 0.0179 = 1.8%

6. a. 0.0571 1/0.0571 is approximately 17.5

b. 0.1401 1/0.1401 = 7.1

7. 0.8078

8. 0.0049

9. 0.0823

10. a. 0.7053 b. 0.7064 c. 0.7155

11. a. 0.8185 = 81.85% b. 0.0228 = 2.28%

12. 0.0015 Chapter 7

1. a. approximately normal b. $31.65 c. $1.00

2. a. approximately normal. b. 62 cents c. 0.778

3. a. 6.75 b. 0.17678 = 0.18 c. approximately normal

4. a. 0.2743 b. 0.0359 c. Yes

5. a. 0.0181 b. 0.0468 c. 0.849

6. a. 0.6390 b. With n = 250, CLT holds. c. If normal, the median is approximately equal to the mean. d. Probably not; salaries typically skewed. e. If mean is higher, probability will be less than calculated value.

7. a. 0.1335 b. 0.6214 c. 0.0559 d. n = 100 8. a & b.

Vote For A Woman President?

Yes 80 No 70 e g a

t 60 n e c

r 50 e P 40

10 1940 1950 1960 1970 1980 1990 Year

c. Yes. Percentage of yeses steadily rise, no’s steadily decrease.

d. high eighties or in the nineties

f. study the variability of a sample statistic

9. 0.9992

10. 0.0007 Chapter 8

1. a. 55.20 b. 8.546 c. 46.654 to 63.746

2. a. $5173.97 to $6026.03 b. lower level of confidence

3. Ha: µ ¹ 10.00, z* = (9.1 - 10)/(5/) = -1.27, P = 2×(0.5000 - 0.3980) = 0.2040, Fail to reject Ho

4. a. mean gestation period b. Ha: µ  44 c. normality is assumed, n = 81 d. n = 81, x = 42.5 e. z* = (42.5 - 44)/(5/ 81 ) = -2.70 ±z(0.025) = ±1.96 f. Reject Ho

5. a. Variable N Mean Median StDev Minimum Maximum Q1 Q3 Amount 150 64.17 50.00 50.29 0.00 300.00 25.00 100.00

Cost of Holiday Decorations

c 30 n e u q

e 20 r F

0 100 200 300 Amount

b. 52.96 to 75.37 c. mu not = 59.00, z* = 0.90; P = 0.37 or z  -1.96, z  1.96; fail to reject Ho d. normality can be assumed, CLT with n = 150 Chapter 9

1. a. 2.965 to 4.655 b. Does not, x most likely is not normal

2. x = 86.0, s = 11.84, 79.15 to 92.85

3. a. x = 11.49, s = 0.47 b. 11.23 to 11.75

4. x = 18.975, s = 3.312, se mean = 0.585 Ho: µ = 18% vs. Ha: µ ¹ 18% t* = 1.67, P = 0.11; t  -2.04, t  2.04 Fail to reject Ho

5. a. 0.21 b. 0.043

6. 0.37 to 0.43

7. 0.015

8. 0.085 to 0.095

9. a. n = 100: 0.0588, 0.08982, 0.098, 0.08982, 0.0588

n = 500: 0.0263, 0.0402, 0.0438, 0.0402, 0.0263

n = 1000: 0.0186, 0.0284, 0.03099, 0.0284, 0.0186

n = 1500: 0.0152, 0.0232, 0.0253, 0.0232, 0.0152

b. symmetric about 0.5

10. a. 915 b. 229 c. 1825 d. Increasing the maximum error decreases the sample size. e. Increasing the level of confidence increases the sample size.

11. 522 12. a. 0.82 b. 1005 c. 355 d. 273 e. ¼ the original size.

13. 4626

14. a. z* = -2.53 b & c. Ho: p = 0.50 (³) vs. Ha: p < 0.50 z* = -2.53, P = 0.0057, z(0.01) = -2.33 Reject Ho

15. a. 22

Last Month's Earnings

c 3 n e u q

e 2 r F

0 100 200 300 400 500 600 700 800 x

Sample mean = $326.10 Sample standard deviation = $164.43 c.

Histogram of Earnings, with Normal Curve

4 y c n

e 3 u q e r

0 100 200 300 400 500 600 700 800 Earnings

The histogram clearly suggests that this set of data is approximately normally distributed. d. 326.1; $253.20 to $399.00

e. Ha: µ ¹ 350, t* = -0.68, 0.492 < P < 0.556, ±t(21, 0.025) = ±2.08 Fail to reject Ho

16. Ha: µ > $10, t* = 3.57, P < 0.005, t(24, 0.01) = 2.49 Reject Ho

17. Ha: µ > 21, t* = 2.52, P = 0.01, t(21, 0.05) = 1.72 Reject Ho

18. a. n = 800; trial = one person; success = not prosecute; p = P(success); x = 0, 1, 2, ... , 800 b. proportion of sample; from sample; statistic. c. 0.033 d. same when rounded

19. a. 0.027 c. 2213

20. a. Maximum error of estimate b. 1025 Chapter 10

1. a. d = -1.264, sd = 2.798; -2.414 to –0.114 b. The market had not recovered.

2. d = 26.3, sd = 24.5 Ho: µd = 0 vs. Ha: µd > 0 (improvement) t* = 3.39 P < 0.005, t  1.83 Reject Ho

3. A: x = 6.0, s² = 1.333 B: x = 4.0, s² = 2.667 0.22 to 3.78

4. a. 1.36 to 4.64 b. Sample sizes large enough

5. Ho: µ2 - µ1 = 0 vs. Ha: µ2 - µ1 > 0 (µ1 < µ2) t* = 2.84 0.008 < P < 0.012, t(9, 0.05) = 1.83 Reject Ho

6. Ho: p1 – p2 = 0 vs. Ha: p1 - p2 ¹ 0 z* = 1.75 P = 0.0802, z(0.025) = 1.96 Fail to reject Ho

7. a. Ho: pm - pw = 0 vs. Ha: pm - pw ¹ 0 z* = 1.37 P = 0.1706, z  -1.96 and z  1.96 Fail to reject Ho b. Ho: pu - pc = 0 vs. Ha: pu - pc ¹ 0 z* = 1.58 P = 0.1142, z  -1.96 and z  1.96 Fail to reject Ho

8. Ho: µd = 0 (no difference) vs. Ha: µd ¹ 0 (is different) d = 0.275, sd = 0.429 t* = 2.22 0.040 < P < 0.052, t  -1.80 and t  1.80 Reject Ho

9. Ho: µm - µf = 0 vs. Ha: µm - µf > 0 x m = 33.83, sm2 = 6.38, x f = 26.27, sf2 = 4.02 t* = 8.91 P < 0.001, t  1.81 Reject Ho Chapter 11

1. Ha: There is a difference c²* = 0.34 P = 0.9523, c²  7.82 Fail to reject Ho

2. Ha: The proportions are different per age group. c²* = 3.904 P = 0.273, c²(3,0.05) = 7.82 Fail to reject Ho