Solutions to even numbered assigned problems for Statistics, Eleventh Edition
Chapter 8
8.34
a. The test statistic is -1.7
The rejection region is z>1.28.
There is insufficient evidence to indicate that the true mean cyanide level in soil in The Netherlands exceeds 100 mg/kg.
b. The rejection region is z>1.645.
The rejection region is z>2.33.
For this problem, since the test statistic falls on the opposite side of the mean than the rejection region, we will not reject for any reasonable value of.
8.40
The smallest value which the null hypothesis would be rejected is just greater than .06.
8.42 .03
8.52
a. 0
b. If xbar had been larger, the pvalue would have been larger.
8.72 s=2
The test statistic is .87. Use alpha=.05 to get a t value of 2.92
There is insufficient evidence to indicate that the mean length of the great white sharks off the Bermuda coast is in excess of 21 feet at .
Chapter 9
9.22
The test statistic is t=1.56
The rejection region is t<-2.021 or t>2.021.
There is insufficient evidence to indicate that the mean number of high frequency vocal responses differ for piglets castrated by the 2 methods at .
Chapter 10
10.6
a. The response variable of the study is body mass of birds.
b. The experimental units are the birds.
c. The factor in the study is habitat type. There are 3 levels of habitat type.
d. The treatments are the same as the factor levels in this problem. There are 3 factor levels or treatments: aquatic, ground terrestrial and aerial terrestrial.
10.22
a.
Source / df / SS / MS / FTreatment / 6 / 18.4 / 3.0667 / 4.01
Error / 35 / 26.8 / .7657
Total / 41 / 45.2
b. The number of treatment is 7.
c. The test statistic is F = 4.01
The rejection region is F > 1.98.
There is sufficient evidence to indicate a difference among the population means .
d. The observed significance level is <.01.
10.28
a. participants in the study
b. brand recall score
c. factor= tv viewing group
treatments = 3 levels of the factor
d. means given are only sample means
e. F=20.45 and p value = 0
f. There is evidence of differences in the mean recall scores among the 3 groups.
10.30
b. The sample means are sample means. The next time the experiment is repeated, the sample means could be much different. We cannot tell if the population means are different unless we compute an appropriate test statistic which involves the standard deviation.
c. From the printout, the test statistic is F = 2.5 and the p-value is p = .071. There is sufficient evidence to indicate some differences in the mean ages among the 4 groups.
d. omit
10.42
a. From the diagram, the following pairs of treatments are significantly different because they are not connected by a line: A and E, A and B, A and D, C and E, C and B, C and D, and E and D. All other pairs of means are not significantly different because they are connected by lines.
b. From the diagram, the following pairs of treatments are significantly different because they are not connected by a line: A and B, A and D, C and B, C and D, E and B, E and D, and B and D. All other pairs of means are not significantly different because they are connected by lines.
c. From the diagram, the following pairs of treatments are significantly different because they are not connected by a line: A and E, A and B, and A and D. All other pairs of means are not significantly different because they are connected by lines.
d. From the diagram, the following pairs of treatments are significantly different because they are not connected by a line: A and E, A and B, A and D, C and E, C and B, C and D, E and D and B and D. All other pairs of means are not significantly different because they are connected by lines.
10.44 No significant difference between Division II and Division III coaches. The mean response for Division I coaches is significantly larger than the mean responses for the Division II and Division III coaches.
10.50 MSE=3.01 n1=n2=n3=108 t=2.326 Bonferroni value=.55
No significant difference between S and V ratings. Neutral rating significantly different from S and V.
10.66 c. The p value is < .0001 which indicates evidence of a difference in mean Wong scores among the 9 dimensions. The p value for testing the block means is .152 which indicates no significant difference among the block means.
d. The mean score for WHAT-B differs from HOWA, WHOB and WHOA. The mean score for WHOC and HOWC differ from WHOB and WHOA.
e. The probability of declaring at least one pair of means different when they really are not different is .05.
10.78 a. Factor A has 4 levels and factor B has 2 levels
b. 3
c. Factor A: F=5
Factor B: F=6.33
Interaction: F=2
e. Insufficient evidence of interaction
10.80
a. The treatments for this experiment consist of a level for factor A and a level for factor B. There are 6 treatments.
c. Yes. The test statistic is 36.62. The rejection region is F > 5.14.
There is sufficient evidence to indicate that factors A and B interact to affect the response mean
d. No. Because interaction is present, the tests for main effects are not warranted.
10.100
Source / df / SS / MS / FTreatment / 3 / 36.95 / 12.32 / 7.70
Error / 16 / 25.60 / 1.60
Total / 19 / 62.55
Bonferroni analysis: t=2.583 and Bonferroni value is 2.0664
No significant difference between group 1 and 2
No significant difference between groups 1, 3, and 4.
10.102
a.
Source / Df / SS / MS / FA / 3 / 2.6 / .8667 / 1.11
B / 5 / 9.2 / 1.84 / 2.36
AB / 15 / 46.5 / 3.1 / 3.98
Error / 24 / 18.7 / .7792
Total / 47 / 77.0
b. Factor A has a = 4 levels and factor B has b = 6 levels. The number of treatments is ab = 4(6) = 24. The total number of observations is n = 47+1 = 48. Thus, two replicates were performed.
d. The test statistic is 3.98 The rejection region is F > 2.11.
There is sufficient evidence to indicate factors A and B interact to affect the response means .
Since the interaction is significant, no further tests are warranted.
10.110
a. The response variable in this study is the safety rating of nuclear power plants.
b. There are 3 treatments in this study – the three types of professionals. These three groups are the scientists, the journalists, and the government officials.
c. Ho: m1=m2=m3
Ha:At least two treatment means differ
d. >7.065
e. p-value <.01
10.120
a. To determine if Herd and Season interact: The test statistic is F = 1.2.
The p-value is p > .05. There is insufficient evidence to indicate that herd and season interact.
To determine if the mean home range differs among the four herds: The test statistic is F = 17.2.
The p-value is p < .001.. There is sufficient evidence to indicate that the mean home range differs among the four herds .
To determine if the mean home range differs among the four seasons: The test statistic is F = 3.0.
The p-value is p > .05.. There is insufficient evidence to indicate that the mean home range differs among the four seasons .
b. Yes. Since herd and season do not interact, each main effect factor can be treated separately as if the second factor did not exist.
c. The mean home range for herd MTZ is significantly greater than the mean home range for the herds PLC and LGN. The mean home range for herd QMD is significantly greater than the mean home range for the herds PLC and LGN. No other differences exist.
Chapter 11
11.16
b. Choose y = x+1 since it best describes the relation of x and y.
c.
y / x / /2 / .5 / 1.5 / 2-1.5=.5
1 / 1.0 / 2.0 / 1-2.0=-1.0
3 / 1.5 / 2.5 / 3-2.5=.5
Sum of errors = 0
y / x / /
2 / .5 / 3-.5=2.5 / 2-2.5=-.5
1 / 1.0 / 3-1.0=2.0 / 1-2.0=-1.0
3 / 1.5 / 3-1.5=1.5 / 3-1.5=1.5
Sum of errors = 0
d. SSE for 1st model:
SSE for 2nd model:
The best fitting straight line is the one that has the smallest least squares. The model y = 1+x has a smaller SSE, and therefore it verifies the visual check in part a.
e. Some preliminary calculations are:
The least squares line is the same as the second line given.
11.20 a. negative
b. negative
c. women
d. No. It is outside the observed values of x.
11.34 The graph in b would have the smallest because the width of the data points is the smallest.
11.36
a. s2=.0429 b. s= .2071 c. most observations should be within 2s of the l.s. line
11.40
a. SSE=858.174 s2=286.058, s=16.913
b. We would expect most of the observations to be within 2s of the least squares line.
b.
c. We would expect most of the observations to be within 2s of the least squares line. This is:
11.66
a. The slope is positive.
b. The slope is negative.
c. If r = 0, there is a 0 slope.
d. The relationship between x and y could be either positive or negative.
11.88
The statement is false.
11.108 a. The least square line is .
c. SSE=57.2
d.
e. We are 90% confident the change in the mean value of y for each unit change in x is between -2.101 and -1.099.
f. The 90% confidence interval is (6.151, 20.009)
g. The 90% prediction interval is (5.218, 20.942)
11.112
b. yes
c. yhat= 184 + 1.20x
The estimated y intercept is 184. Since 0 is not in the observed range of x values, the y intercept has no meaning.
The estimated slope is 1.20 For each additional dollar of appraised value the mean selling price is estimated to increase by 1.20 dollars.
d. t= 53.70 and pvalue= 0/2=0 There is evidence of a positive linear relationship.
e. r2=.974 97.45% of the variability of sale price is explained by its linear relationship with appraised value. r= .987
f. (390,085 to 569,930) We are 95% confident the actual selling price for a home appraised at $400,000 is between $390,085 and $569,930.
11.114 a. Since 0 is not in the observed range of x values, the y intercept has no meaning.
b. For each additional increase of 1% of land covered by the plants, the mean standing crop increases by and estimated .089 gram per meter squared.
c. > .042
Chapter 12
12.6
a. .
b. .
c. SSE = 151,016, MSE = 8883, s = Root MSE = 94.251
We expect about 95% of the y-values to fall within or or units of the fitted regression equation.
d.
From the printout, the test statistic is t = -3.42.
The rejection region is t < -2.110 or t >2.110.
There is sufficient evidence to indicate at .
e.
f. R2= 45.9% of the sample variation of the y values is explained by the model.
g. The test statistic is
OR
The test statistic is
h. The observed significance level is p = .005. Using =.05, there is sufficient evidence to indicate that the model is useful in predicting the value of y.
12.26
To determine if the model is useful , we test:
At least one
The test statistic is
The rejection region is F > 247.
There is insufficient evidence to indicate the model is adequate at .
12.32
a. We are 95% confident that the actual heat rate will be between 11,599.6 and 13,665.5 when the speed is 7500 rpm, the inlet temp is 1000, the exhaust temp is 525, the cycle pressure ratio is 13.6 and the air flow rate is 10.0.
b. We are 95% confident that the mean heat rate will be between 12,157.9 and 13,107.1 when the speed is 7500 rpm, the inlet temp is 1000, the exhaust temp is 525, the cycle pressure ratio is 13.6 and the air flow rate is 10.0.
c. Yes
12.40
a. R2=.956 95.6% of the total variability of the y values is explained by this model.
b.
The test statistic is F=202.8
RR: F> 2.95.
There is sufficient evidence that the model is adequate for predicting y at .
d.
T.S: t=2.5.
RR: t < -2.048 or t > 2.048.
There is sufficient evidence to indicate that and interact at .
12.70
a. yhat=80 + 16.8x1 +40.4x2
b. = µ2-µ1 and β2= µ3-µ1
c. Ho: µ1=µ2=µ3
d. F=24.72 with a RR of F>3.89. There is evidence at least one of the means is different
12.80
a.