Chapter 13
13.1a Equal-variances estimator
= (524 – 469) 2.009
= 5573.87
b Equal-variances estimator
= (524 – 469) 2.009
= 55146.33
c The interval widens.
d Equal-variances estimator
= (524 – 469) 1.972
= 5536.26
e The interval narrows.
13.2 = 0
0
a Equal-variances test statistic
Rejection region: –2.074 or 2.074
= = .43, p-value = .6703. There is not enough evidence to infer that the population means differ.
b Equal-variances test statistic
Rejection region: –2.074 or 2.074
= = .04, p-value = .9716. There is not enough evidence to infer that the population means differ.
c The value of the test statistic decreases and the p-value increases.
d Equal-variances test statistic
Rejection region: –1.960 or 1.960
= = 1.53, p-value = .1282. There is not enough evidence to infer that the population means differ.
e The value of the test statistic increases and the p-value decreases.
f Rejection region: –2.074 or 2.074
= = .72, p-value = .4796. There is not enough evidence to infer that the population means differ.
g The value of the test statistic increases and the p-value decreases.
13.3 a Unequal-variances estimator
= 64.8 (rounded to 65, approximated by)
= (63 – 60) 1.667= 3 4.59
b Unequal-variances estimator
= 63.1 (rounded to 63, approximated by)
= (63 – 60) 1.671= 3 10.38
c The interval widens.
d Unequal-variances estimator
= 131 (approximated by)
= (63 – 60) 1.656= 3 3.22
e The interval narrows.
13.4 = 0
0
a Unequal-variances test statistic
= 200.4 (rounded to 200)
Rejection region:
= = .62, p-value = .2689. There is not enough evidence to infer that is greater than.
b Unequal-variances test statistic
= 223.1 (rounded to 223)
Rejection region:
= = 2.46, p-value = .0074. There is enough evidence to infer that is greater than.
c The value of the test statistic increases and the p-value decreases.
d Unequal-variances test statistic
= 25.6 (rounded to 26)
Rejection region:
= = .23, p-value = .4118. There is not enough evidence to infer that is greater than.
e The value of the test statistic decreases and the p-value increases.
f Unequal-variances test statistic
Rejection region:
= = .35, p-value = .3624. There is not enough evidence to infer that is greater than.
g The value of the test statistic decreases and the p-value increases.
13.5 a Equal-variances t-test degrees of freedom = 28, Unequal-variances t-test degrees of freedom =26.4
b Equal-variances t-test degrees of freedom = 24, Unequal-variances t-test degrees of freedom = 10.7
c Equal-variances t-test degrees of freedom = 98 , Unequal-variances t-test degrees of freedom = 91.2
d Equal-variances t-test degrees of freedom = 103, Unequal-variances t-test degrees of freedom = 78.5
13.6 a In all cases the equal-variances t-test degrees of freedom is greater than the unequal-variances t-test degrees of freedom.
13.7 = 0
< 0
Two-tail F test: F = 1.02, p-value = .9856; use equal-variances test statistic
Rejection region:
= p-value = .3382. The manager should choose to use cameras.
13.8 = 0
< 0
Two-tail F test: F = 1.02, p-value = .9823; use equal-variances test statistic
Rejection region:
= p-value = .0283. There is enough evidence to infer that there are fewer errors when the yellow ball is used.
13.9 = 0
0
Two-tail F test: F = .11, p-value = .0106; use unequal-variances test statistic
= 8.59 (rounded to 9)
Rejection region: or
= p-value = .8123. There is not enough evidence to infer that the two groups differ in the number of pictures printed.
13.10 = 0
0
Two-tail F test: F = 1.04, p-value = .9873; use equal-variances test statistic
Rejection region: or
= p-value = .1368. There is not enough evidence to infer a difference between the two types of vacation expenses.
13.11a = 0
> 0
Two-tail F test: F = 1.59, p-value = .3050; use equal-variances test statistic
Rejection region:
== 4.61, p-value = 0. There is enough evidence to infer that Tastee is superior.
b = (36.93 – 31.36) 2.021
= 5.572.43; LCL = 3.14, UCL = 8.00
c The histograms are somewhat bell shaped. The weight gains may be normally distributed.
13.12 = 0
0
Two-tail F test: F = .99, p-value = .9571; use equal-variances test statistic
Rejection region: or
= p-value = .1204. There is not enough evidence to infer that oat bran is different from other cereals in terms of cholesterol reduction?
13.13 a = 0
0
Two-tail F test: F = .50, p-value = 0; use unequal-variances test statistic
= 449
Rejection region: or
= = 1.79, p-value = .0734. There is not enough evidence to conclude that a difference in mean listening times exist between the two populations.
b = (58.99 –52.96) 1.960= 6.036.59;
LCL = –.56, UCL = 12.62
c The histograms are bell shaped.
13.14 a = 0
> 0
Two-tail F test: F = 1.01, p-value = .9619; use equal-variances test statistic
Rejection region:
= p-value = .0021. There is enough evidence to infer that the cruise ships are attracting younger customers.
b = (59.81 – 57.40) 2.576
= 2.412.16;
LCL = .25, UCL = 4.57
13.15a = 0
0
Two-tail F test: F = .98, p-value = .9254; use equal-variances test statistic
Rejection region: or
= = 1.40, p-value = .1640. There is not enough evidence to infer that the distance males and females drive differs.
b = (10.23 – 9.66) 1.972
= .57.80; LCL = –.23, UCL = 1.37
c The histograms are bell shaped.
13.16 = 0
0
Two-tail F test: F = .98, p-value = .9520; use equal-variances test statistic
Rejection region:
=p-value = .1753. There is not enough evidence to retain supplier A - switch to supplier B.
13.17 = 0
0
Two-tail F test: F = .92, p-value = .5000; use equal-variances test statistic
Rejection region: or
=p-value = .8759. There is no evidence of a difference in job tenures between men and women.
13.18a = 0
0
Two-tail F test: F = 5.18, p-value = .0019; use unequal-variances test statistic
= 33.9 (rounded to 34)
Rejection region: or
= p-value = .0060. There is enough evidence to conclude that the two packages differ in the amount of time needed to learn how to use them.
b = (70.42 –56.44) 2.030= 13.989.67;
LCL = 4.31, UCL = 23.65
c The amount of time is required to be normally distributed.
d The histograms are somewhat bell shaped.
13.19a = 0
< 0
Two-tail F test: F = 5.18, p-value = .0019; use unequal-variances test statistic
= 276.5 (rounded to 277)
Rejection region:
= = –11.60, p-value = 0. There is enough evidence to infer that the amount of time wasted in unsuccessful firms exceeds that of successful firms.
b = (5.02 – 7.80) 1.960= –2.78.47;
LCL = –3.25, UCL = –2.31. Workers in unsuccessful companies waste on average between 2.31 and 3.25 hours per week more than workers in successful companies.
13.20 = 0
0
Two-tail F test: F = .73, p-value = .0699; use equal-variances test statistic
Rejection region:
= = 7.54, p-value = 0. There is enough evidence to conclude that the reaction time of drivers using cell phones is slower that for non-cell phone users.
13.21 = 0
0
Two-tail F test: F = 1.10, p-value = .6406; use equal-variances test statistic
Rejection region: or
= = –1.17, p-value = .2444. There is not enough evidence to infer that the type of discussion affects reaction times.
13.22 = 0
> 0
Two-tail F test: F = .97, p-value = .9054; use equal-variances test statistic
Rejection region:
== .90, p-value = .1858. There is not enough evidence to infer that people spend more time researching for a financial planner than they do for a stock broker.
13.23 = 0
< 0
Two-tail F test: F = .74, p-value = .0446; use unequal-variances test statistic
= 373
Rejection region:
= = –4.69, p-value = 0. There is enough evidence to infer that students without textbooks outperform those with textbooks.
13.24 = 0
0
Two-tail F test: F = .85, p-value = .2494; use equal-variances test statistic
Rejection region: or
= = –2.05, p-value = .0412. There is enough evidence to conclude that there are differences in service times between the two chains.
13.25 = 0
0
Two-tail F test: F = .71, p-value = .1214; use equal-variances test statistic
Rejection region: or
= = 2.65, p-value = .0087. There is enough evidence to conclude that the two types of specialties differ in the time devoted to patients.
13.26 a = 0
0
Two-tail F test: F = 1.51, p-value = .0402; use unequal-variances test statistic
= 190
Rejection region: or
= = 1.16, p-value = .2467. There is not enough evidence to infer that differences exist between the two types of customers.
13.27 = 0
> 0
Two-tail F test: F = 1.07, p-value = .8792; use equal-variances test statistic
Rejection region:
== .91, p-value = .1849. There is not enough evidence to infer that the new design tire lasts longer than the existing design tire.
13.28
< 0
Two-tail F test: F = .95, p-value = .8252; use equal-variances test statistic
Rejection region:
== −2.09
t =, p-value = .0189. There is enough evidence to conclude that commission salespeople outperform fixed-salary salespersons
13.29
0
Two-tail F test: F = .88, p-value = .4709; use equal-variances test statistic
Rejection region: and
== −4.58
t = −4.58, p-value = 0. There is enough evidence to conclude there is a difference in scores between those who have and those who do not have accidents in a three-year period.
13.30 = 0
0
Two-tail F test: F = .41, p-value = 0; use unequal-variances test statistic
= 222
Rejection region:
= = 6.28, p-value = 0. There is enough evidence to conclude that bottles of wine with metal caps are perceived to be cheaper.
13.31 The data are observational. Experimental data could be produced by randomly assigning babies to either Tastee or the competitor’s product.
13.32 Assuming that the volunteers were randomly assigned to eat either oat bran or another grain cereal the data are experimental.
13.33 The data are observational. It is not possible to conduct a controlled experiment.
13.34 a The data are observational because the students decided themselves which package each would use.
b The professor can randomly assign one of the two packages to each student.
c Better students tend to choose Program B and better students learn how to use computer software more quickly.
13.35 a The data are observational.
b A powerful dictator can randomly order medical students to either general/family practice or pediatrics.
13.36a Let students select the section they wish to attend and compare test results.
b Randomly assign students to either section and compare test results.
13.37 Randomly assign patients with the disease to receive either the new drug or a placebo.
13.38a Randomly select finance and marketing MBA graduates and determine their starting salaries.
b Randomly assign some MBA students to major in finance and others to major in marketing. Compare starting salaries after they graduate.
c Better students may be attracted to finance and better students draw higher starting salaries.
13.39a The data are observational because to obtain experimental data would entail randomly assigning some people to smoke and others not to smoke.
b It is possible that some people smoke because of a genetic defect (Genetics have been associated with alcoholism.), which may also be linked to lung cancer.
c In our society the experiment described in part a is impossible.
13.40 = 0
0
Rejection region:
p-value = .0073. There is enough evidence to infer that the Brand A is better than Brand B.
13.41 = 0
0
Rejection region:
p-value = .0320. There is enough evidence to infer that ABS is better.
13.42 = 0
0
Rejection region:
p-value = .0473. There is enough evidence to infer that the camera reduces the number of red-light runners.
13.43a = 0
0
Rejection region:
–1.15, p-value = .1375. There is not enough evidence to infer that the new fertilizer is better.
b =; LCL = –2.92, UCL = .92
c The differences are required to be normally distributed
d No, the histogram is bimodal.
e The data are experimental.
f The experimental design should be independent samples.
13.44 a = 0
0
Rejection region:
1.82, p-value = .0484. There is enough evidence to infer that companies with exercise programs have lower medical expenses.
b = ; LCL = –.66, UCL = 6.82
c Yes because medical expenses will vary by the month of the year.
13.45 = 0
0
Rejection region:
1.53, p-value = .0638. There is not enough evidence to infer that mortgage payments have increases in the past 5 years.
13.46 = 0