1. A major home improvement store conducted its biggest brand recognition campaign in
the company's history. A series of new television advertisements featuring well-known
entertainers and sports figures was launched. A key metric for the success of television
advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189
adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The
percentage of a typical television advertisement receiving the "like the ads a lot" score is
believed to be 22%. Company officials wanted to know if there is evidence that the series
of television advertisements are less successful than the typical ad (i.e. if there is
evidence that the population proportion of "like the ads a lot" for the company's ads is
less than 0.22) at a 0.01 level of significance. (1 point)
a. What critical value should the company officials use to determine the rejection
region?
b. What is the lowest level of significance at which the null hypothesis can be rejected?
c. At the 0.01 level of significance, can company officials conclude that the series of
television advertisements are less successful than the typical ad?
a)
Solution:
Critical value is - z(0.01) = -2.326
Answer: -2.326
b)
Solution:
The lowest level of significance at which the null hypothesis can be rejected is the pvalue.
Ho: p ≥ 0.22
Ha: p < 0.22
p-value = P(z < statistic)
statistic =
𝑝̂−𝑝0
√(𝑝𝑜 (1−𝑝0 )/𝑛
=
230
−0.22
1189
√0.22(1−0.22)/1189
= −2.211
p-value = P(z<-2.211) = 0.0135
Answer: 0.0135
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c)
Answer: Since the p-value is greater than 0.01 we don´t reject Ho, we do not
have enough evidence to conclude that the series of television advertisements are
less successful than the typical ad
2. The lumen output was determined for each of c = 3 different brands of 60-Watt softwhite light bulbs, with 8 bulbs of each brand tested. The sums of squares were computed
as SSW = 4773.3 and SSA = 591.2. Use the F test of ANOVA (assume α = 0.05) to
decide whether or not there are any differences in true average lumen outputs between the
three brands for this type of light bulb. (1 point)
Solution:
Test: ANOVA
Ho: 1=2=3
Ha: 1, 2 and 3 are not equal
Statistic F = [SSA/(c-1)]/[SSW/(N-c)] = [(591.2/2)/(4773.3/21)] = 1.3
Critical value = FINV (0.05,2,21) = 3.467
Rejection region = {x / x > 3.467}
Decision: since the statistic value is not greater than 3.467 we do not rejuect Ho
Answer: At  =0.05 we do not have enough evidence to conclude that there are any
differences in true average lumen outputs between the three brands for this type of light
bulb.
3. A realtor wants to compare the mean sales-to-appraisal ratios of residential properties
sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from
each neighborhood and the ratios recorded for each, as shown below.
A:
1.2, 1.1, 0.9, 0.4
C:
1.0, 1.5, 1.1, 1.3
B:
2.5, 2.1, 1.9, 1.6
D:
0.8, 1.3, 1.1, 0.7
What should be the decision for the Levene's test for homogeneity of variances at a 5%
level of significance? (1 point)
4. As part of an evaluation program, a sporting goods retailer wanted to compare the
downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and
determined their maximum downhill speeds. The results are presented in miles per hour
in the table below. (1 point)
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Trial
1
2
3
Barth
43
46
43
Tornado
37
38
39
Reiser
41
45
42
Shaw
43
45
46
Construct the ANOVA table from the sample data. What would be the decision in this
case, accept or reject the null hypothesis?
5. Family transportation costs are usually higher than most people believe because those
costs include car payments, insurance, fuel costs, repairs, parking, and public
transportation. Twenty randomly selected families in four major cities are asked to use
their records to estimate a monthly figure for transportation cost. (1 point)
a. Use the data obtained and one-way ANOVA to test whether there is a significant
difference in monthly transportation costs for families living in these cities. Assume
that α = 0.05.
Atlanta
$850
680
750
800
875
New York
$450
725
500
375
700
Los Angeles
$1050
900
1150
980
800
Chicago
$740
650
875
750
800
b. Doing a multiple comparisons test on the data (α = 0.05), which pairs of cities, if any,
have significantly different mean costs?
6. How different are the rates of return of money market accounts and certificates of deposit
that vary in length of their term? The data in the Excel MMCDRate contain these rates
for banks in a suburban area. (2 points)
a. At the 0.05 level of significance, determine whether there is evidence of a difference
in the mean rates for these investments.
b. If appropriate, us the Tukey procedure to determine which investments differ (use α =
0.05).
MMCDRATE EXCEL
Bank
Astoria Federal
Bank of America
Bethpage Federal Credit Union
BNB Bank
Brooklyn Federal
Citibank
Money
Market
0.10
0.15
0.80
0.85
0.65
0.40
One Year
Two Year
Five Year
CD
CD
CD
0.75
0.75
2.75
0.40
0.85
2.25
1.30
1.80
3.00
1.25
1.99
3.02
1.00
1.60
2.95
0.80
1.15
2.25
3
Discover
Emigrant
Empire National
Flushing
Hudson City
Madison National
NY Commercial
NY Community
Queens County
Ridgewood Savings
Roslyn Savings
Sovereign
Sterling National
Wachovia
1.20
0.70
0.75
1.00
1.00
0.75
0.50
0.20
0.50
0.25
0.20
0.20
1.30
0.02
1.50
1.00
1.16
0.50
1.25
0.85
1.00
1.00
1.00
1.05
1.00
0.65
0.75
0.40
1.90
1.55
1.76
0.50
1.85
1.50
1.25
1.25
1.25
1.50
1.25
0.69
1.25
0.70
2.95
2.80
2.53
1.00
3.15
2.80
1.70
1.70
1.70
3.00
1.70
1.99
1.75
1.06
7. A student team in a business statistics course performed a factorial experiment to
investigate the time required for pain-relief tablets to dissolve in a glass of water. The
two factors of interest were brand name (Equate, Kroger, or Alka-Seltzer) and water
temperature (hot or cold). The experiment consisted of four replicates for each of the six
factor combinations. The data are shown in the Excel file PainRelief, and show the time
a tablet took to dissolve (in seconds) for the 24 tablets used in the experiment. (2 points)
PAIN RELIEF EXCEL
Temperature Equate Kroger
Cold
85.87 75.98
Cold
78.69 87.66
Cold
76.42 85.71
Cold
74.43 86.31
Hot
21.53 24.10
Hot
26.26 25.83
Hot
24.95 26.32
Hot
21.52 22.91
AlkaSeltzer
100.11
99.65
100.83
94.16
23.80
21.29
20.82
23.21
The null and alternative hypotheses would be:
H0: There is no interaction between brand and water temperature
H1: There is an interaction between brand and water temperature
At the 0.05 level of significance;
a. Is there an interaction between brand of pain reliever and water temperature?
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b. Is there an effect due to brand?
c. Is there an effect due to water temperature?
d. Plot the mean dissolving time for each brand for each water temperature.
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