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252hwkadd 12/01/03 (Open this document in 'Print Layout' view!) Roger Even Bove
PROBLEMS THAT APPEAR IN THE 9TH EDITION BUT NOT THE 8TH (and some from the 8th or other places. )
9.40 Suppose that in a one-tail hypothesis test where you reject H 0 only in the lower tail, you compute the value of the test statistic
z as 1.38, what is the p-value?
9.41 In Problem 9.40, what would be your statistical decision if you tested the null hypothesis at the 0.01 level of significance?
9.66 In a national poll of 811 personal computer owners, Peter D. Hart Research Associates found that 44% (357) of the PC owners
ranked sharing their credit card information as the number one concern in on-line shopping. The survey also indicated that 72% (584)
of PC owners would purchase a more secure computer if available. When given the actual dollar amount the added security would cost,
57% (462) indicated that they would pay an extra $75 for a new PC delivering a more secure on-line experience.
a. Test the null hypothesis that 50% of all PC owners in the United States rank sharing their credit card information as the
number one concern in on-line shopping versus the alternative that the percentage is not equal to 50% .05
b. Compute the p-value in(a) and interpret its meaning.
c. At the .05 level of significance, is there evidence that more than half of all PC owners in the United States would pay an
extra $75 for a new PC delivering as more secure on-line experience?
d. Compute the p-value in(c) and interpret its meaning.
e. At the .05 level of significance, is there evidence that more than 55% of all PC owners in the United States would pay an
extra $75 for a new PC delivering as more secure on-line experience?
f. Compute the p-value in(e) and interpret its meaning.
9.67 To handle the increased necessity of storing and organizing huge amounts of data, many companies are making large
expenditures for increased data-storage expenditures. The slowdown in the US economy, however, has many companies delaying data
storage expenditures. In July 2001, it was reported that 38% of the companies surveyed have delayed expenditures on storage
deployments because of the economic slowdown. The sample size of this survey was not disclosed.
a. Suppose that the above results were based on the responses of 50 companies. Is there evidence at the .01 level of
significance that less than half of all companies are delaying data-storage expenditures?
b. Compute the p-value in(a) and interpret its meaning.
c. Suppose that the above results were based on the responses of 100 companies. Is there evidence at the .01 level of
significance that less than half of all companies are delaying data-storage expenditures?
d. Compute the p-value in(c) and interpret its meaning.
e. Compare your answers in (a) and (b) with your answers to (c) and (d). Explain the effect that sample size has on statistical
significance.
f. What ethical issues are raised when one fails to report the sample size used in a survey?
10.32 HomeGrocer.com vs. local Seattle supermarkets.
Products HomeGrocer Supermarkets
1 Tide High Efficiency, 64 oz. 6.99 6.99
2 Oreo Cookies, 20 oz. 3.29 3.49
3 Formula 409 Cleaner, 22 oz. 2.59 2.69
4 Pampers Newborn Diapers, 40 count 10.79 10.99
5 Coke Classic, dozen 12 oz. Cans 3.99 3.59
6 Colgate Total Toothpaste, 7.8 oz. 3.49 3.49
7 Tropicana Orange Juice, 64 oz. 3.59 3.49
8 Cheerrios Whole Grain Cereal, 20 oz. 4.29 3.99
a. At the 0.05 level, is there evidence of a difference in the average price for products purchased from the two vendors?
b. Compute the p-value in(a) and interpret its meaning.
c. Set up a 95% confidence interval estimate of the difference in the average price for products purchased from the two
vendors?
d. Compare the results in (a) and (c).
12.7 Of 56 white workers terminated, 29 claimed bias. Of 407 black workers terminated, 126 claimed bias.
a. At the 5% significance level, is there evidence that white workers are more likely to claim bias than black workers?
b. Find and interpret the p-value in a.
12.8 500 African Americans and 500 whites (all with incomes above $50000) were surveyed with the result that 74% of the African-
Americans and 84% of the whites owned stocks.
a. At the 5% significance level, is there a significant difference between the proportion of African Americans and the
proportion of whites who own stocks?
b. Find and interpret the p-value in a.
c. Set up a 95% confidence interval for the difference between the two proportions.
D6a Given: H 0 : 1 2 , H 1 : 1 2 , n1 16, n 2 21, s1 100 and s 2 400 . Test the hypotheses using only right tail
2 2 2 2 2 2
tests. .05 .
12.23 The results of a Gallup phone survey appear below. Consumers were asked if they objected to having their medical records
shared with different types of organizations. Results follow.
O Ins Cos Pharm Research
Yes 820 590 670
No 180
410 330
a) Is the proportion of people who object different for different institutions? .05.
b) If appropriate, use the Marascuilo procedure to determine which organizations are different. Discuss.
12.49 The manager of a computer network has the following data on service interruptions per day over the last 500 days. Does it
follow a Poisson distribution? .01
Interruptions Number
per day of days
0 160
1 175
2 86
3 41
4 18
5 12
6 8
Total 500
12.52 A random sample of 500 car batteries revealed the following distribution of battery life in years. If x 2.80 and s 0.97,
does it follow a Normal distribution? .05
Life Frequency
0 under 1 12
1 under 2 94
2 under 3 170
3 under 4 188
4 under 5 28
5 under 6 8
Total 500
14.4 Computer Output.
————— 11/20/2003 11:23:07 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > Retrieve "C:\Berenson\Data_Files-9th\Minitab\Warecost.MTW".
2
Retrieving worksheet from file: C:\Berenson\Data_Files-9th\Minitab\Warecost.MTW
# Worksheet was saved on Mon Apr 27 1998
Results for: Warecost.MTW
MTB > Regress c1 2 c2 c3;
SUBC> Constant;
SUBC> VIF;
SUBC> Brief 3.
Regression Analysis: DistCost versus Sales, Orders Minitab regression Output.
The regression equation is
DistCost = - 2.73 + 0.0471 Sales + 0.0119 Orders
Predictor Coef SE Coef T P VIF
Constant -2.728 6.158 -0.44 0.662
Sales 0.04711 0.02033 2.32 0.031 2.8
Orders 0.011947 0.002249 5.31 0.000 2.8
S = 4.766 R-Sq = 87.6% R-Sq(adj) = 86.4%
Analysis of Variance
Source DF SS MS F P
Regression 2 3368.1 1684.0 74.13 0.000
Residual Error 21 477.0 22.7
Total 23 3845.1
Source DF Seq SS
Sales 1 2726.8
Orders 1 641.3
Obs Sales DistCost Fit SE Fit Residual St Resid
1 386 52.950 63.425 1.332 -10.475 -2.29R
2 446 71.660 63.755 1.511 7.905 1.75
3 512 85.580 84.820 1.656 0.760 0.17
4 401 63.690 67.082 1.332 -3.392 -0.74
5 457 72.810 70.127 0.999 2.683 0.58
6 458 68.440 67.796 1.193 0.644 0.14
7 301 52.460 49.839 2.134 2.621 0.62
8 484 70.770 77.528 1.139 -6.758 -1.46
9 517 82.030 84.196 1.525 -2.166 -0.48
10 503 74.390 77.503 1.126 -3.113 -0.67
11 535 70.840 75.199 1.838 -4.359 -0.99
12 353 54.080 48.800 2.277 5.280 1.26
13 372 62.980 62.311 1.483 0.669 0.15
14 328 72.300 65.626 2.847 6.674 1.75
15 408 58.990 63.852 1.152 -4.862 -1.05
16 491 79.380 75.145 1.069 4.235 0.91
17 527 94.440 88.789 2.004 5.651 1.31
18 444 59.740 59.407 2.155 0.333 0.08
19 623 90.500 87.302 2.535 3.198 0.79
20 596 93.240 93.867 2.097 -0.627 -0.15
21 463 69.330 70.087 1.049 -0.757 -0.16
22 389 53.710 59.898 1.349 -6.188 -1.35
23 547 89.180 87.401 1.657 1.779 0.40
24 415 66.800 66.535 1.107 0.265 0.06
R denotes an observation with a large standardized residual
MTB > Print c1-c3
Data Display Original Data
Row DistCost Sales Orders
1 52.95 386 4015
2 71.66 446 3806
3
3 85.58 512 5309
4 63.69 401 4262
5 72.81 457 4296
6 68.44 458 4097
7 52.46 301 3213
8 70.77 484 4809
9 82.03 517 5237
10 74.39 503 4732
11 70.84 535 4413
12 54.08 353 2921
13 62.98 372 3977
14 72.30 328 4428
15 58.99 408 3964
16 79.38 491 4582
17 94.44 527 5582
18 59.74 444 3450
19 90.50 623 5079
20 93.24 596 5735
21 69.33 463 4269
22 53.71 389 3708
23 89.18 547 5387
24 66.80 415 4161
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\Warecost.MTW";
SUBC> Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\Warecost.MTW
MTB > Stop.
13.36 Suppose that you are testing the null hypothesis that there is no relationship between x and y . Assume n 20 and that
SSR 60 and SSE 40 .
a. What is the value of the F test statistic?
b. At the 5% significance level what is the critical value of F?
c. Based on the answers to a) and b) what statistical decision should be made?
d. Calculate the correlation coefficient from R 2 by assuming that the slope b1 is negative.
e. At the 5% significance level, is there significant correlation between x and y ?
4
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