Homework 12
1. Amos wants to test if increasing the volume on his speakers will decrease a computer’s bit rate.
He has pieces of his ANOVA table from his regression. (Assume the assumptions for regression
have been met). Fill in the six missing values on the table.
df
Model
Error
Total
SS
5.8644
MS
F
3.240
P-value
0.075
97
2. Ross thinks the four people who sit next to him in class spend the same amount of money on their
haircut. To find out he keeps track of how much their haircuts cost for the next couple of months.
Assuming the cost of a haircut is random and that the sample sizes are large enough to assume
normality, and that the variances are the same for all four people, test if the average cost is equal
for all four people (the tip is included in the price).
Use all 7 steps of the hypothesis procedure and use α=0.05.
Name
Tomson
Lawrence
Julien
Ty
ANOVA
Group
Residual
Total
df
Number of
Haircuts
33
35
41
32
SS
Average
Cost
18
11
13
14
Standard deviation for
one haircut
11
10
8
12
MS
F
P-value
Missing
15178.6
For your information, the pooled standard deviation is 10.215. The table below shows the values for the F
distribution (in other words, the critical F which has 0.05 in the right tail. This can be used instead of a pvalue in step 5 to decide whether to reject or not). The first small number is the degrees of freedom for
groups, second is the degrees of freedom for error, and the third is 0.05 for alpha.
F1,1,.05= 161.4
F1,31,.05= 4.16
F1,137,.05= 3.91
F2,1,.05= 199.5
F2,31,.05= 3.305
F2,137,.05= 3.062
F3,1,.05= 215.7
F3,31,.05= 2.911
F3,137,.05= 2.671
F4,1,.05= 224.6
F4,31,.05= 2.679
F4,137,.05= 2.438
3. Ablative spray paint is used on government buildings because it helps make the walls stronger to
resist terrorist attacks. It has been suggested in recent literature that it may be a fire hazard. To
test these claims civil engineers are going select 1000 walls and randomly choose some to be
covered with ablative spray paint. They will throw grenades at each wall and record whether the
wall catches fire.
Assume you are asked to select and alpha other than 0.05. Choose your alpha and explain why.
4. Kyle surveys 500 people and records their gender and if they are a vegetarian.
His data is shown below. Test whether gender is related to being a vegetarian.
Male
Female
Vegetarian
22
28
50
Not a vegetarian
218
232
450
240
260
500
5. TAMU admissions board believes the score you get on the SAT in high school can help
predict your college GPA. Below is a regression model using the SAT scores and GPA for
100 college graduates. Calculate a 98% Confidence Interval for the slope of the
regression line.
(Note: The SAT scores have been divided
by 100 just to make the numbers nicer
Simple linear regression results:
Dependent Variable: GPA
Independent Variable: SAT/100
GPA = 1.3186783 + 0.11072124 [SAT/100]
Sample size: 100
R (correlation coefficient) = 0.7751
R-sq = 0.6007698
Estimate of error standard deviation: 0.1911169
Parameter estimates:
Parameter
Estimate
Intercept
1.3186783 0.16711824 98 7.8906903 <0.0001
Slope
Std. Err.
DF
T-Stat
0.11072124 .091174900 98 1.2143823
P-Value
0.1244
6. Santa wants to use regression to learn how sleigh weight affects reindeer speed. He uses 20
different weights, and measures the reindeer speed at each weight. The output from his
regression is below. When he did SSE, SSR, and SST, Santa calculated those with n=20 by hand.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.759706825
R Square
0.577154460
Adjusted R Square
0.553663041
Standard Error
6.350124954
Average Speed
34.75
(in kilometers/second)
Observations
20
Coefficients
Intercept
Weight (in kilotons)
48.76533
-0.94029
Std Error
3.164064
0.189702
t Stat
P-value
15.41225
-4.95669
8.18E-12
0.000102
Then Santa’s statistical elf pointed out that Santa forgot to include the last data point when he did the
SSR, SSE, and SST by hand (although he did remember to use n=20). What would the correct values be for
SSR, SSE, and SST, if the data point that Santa forgot was: at 19 kilotons speed was 41 kilometers/second.
7. Data was collected for the average number of traffic citations per month given by Officer Smith
and Officer Jones of the Highway Patrol. The last five months were looked at. Officer Smith had
an average of 94 tickets with a standard deviation of 8.7 tickets. Officer Jones had an average of
98.6 tickets with a standard deviation of 6.4 tickets. The standard deviation of the differences in
each month was 1.52 tickets. Using the .05 significance level, test the claim that there is a mean
difference in the number of citations given by the two officers.
8.
Monica believes that the number of musicals a person sees depends on their gender. Houston says it
depends on their age. To find out what really matters they randomly get 80 old women, 90 young women,
75 old men, and 36 young men. Assume the value of the standard deviation for each group should be 2.10,
and the overall average number of musicals is 7.82. Calculate the test statistic if you know that for each
data point
xi
281
  x  7.82 
i 1
i
2
12247
9. Santa wants to know what type of food will make his reindeer calves gain weight. He tries four
different types of food and gets an overall average of 24.93 with a pooled standard deviation of
5.17. Note the p-value was nearly zero. Santa decides to keep feeding his reindeer hay.
Hay
Dog Food
Cat Food
Fish Food
Number of
Calves
4
4
6
6
Standard deviation
(for each calf)
4.6
5.2
4.8
5.8
Mean growth weight (in
pounds)
41.228
34.281
41.228
-8.471
Based on the data show what Santa’s hypothesis test should have looked like assuming normality.
10. You plan to fly from New York to Chicago and have a choice of two flights. You are able to find out
how many minutes late each flight was for a random sample of 25 days over the past few years.
(You have data for BOTH flights on the same 25 days.) For Scairline the average delay is 31
minutes with a standard deviation of 12 minutes. For PilotAirOr the average delay is 48 minutes
with a standard deviation of 20 minutes. The matched pairs standard deviation is 10.1 minutes.
Test whether either flight has a higher average delay assuming normality.
11. Michael is testing 7 different insecticides on fire ants. For each insecticide he sprays a group of 49
fire ants and notes the time it takes for the ants to die. Assume that ant deaths are normally
distributed and each group of ants should have a different standard deviation. Michael then did
an ANOVA test with a 5% significance level and got an F value of 2.02. The computer gave a right
tailed area of 0.062. What conclusion do you think Michael should get from his results?
12. Thomas knows horses live longer than pigs, so he doesn’t need to test it, but he does want a 99%
confidence interval for how much longer they live. Assume the variances for both groups are not
the same. A random sample of each type of animal is shown below. Calculate the 99% confidence
interval.
Horses:
Sample size: 81 horses
Sample average: 15 years
Sample standard deviation: 3.5 years
Pigs:
Sample size: 81 pigs
Sample average: 12 years
Sample standard deviation: 1.2 years
Pooled variance: 6.93
Matched Pairs variance: 2.82
Weighted variance: 5.52
13. Brittany has developed a cure for dogs poisoned with antifreeze, but it doesn’t always work.
One experiment had 19 dogs out of 1000 survive antifreeze poisoning, but now only 16 out of
100 will die. Find a 94% confidence interval (Not Hypothesis test) for the difference in the
percent of dogs that die from antifreeze poisoning with Brittany’s new medicine.
14. Jazz wonders if the height of an engineer determines how many complaints they get. She
surveys the height of engineers. Assume complaints are normally distributed, and that
the variances should be pooled. The engineers are categorized according to whether they
get few, some, or many complaints. The data is shown below. Also is shown some math
that may be helpful.
Test Jazz’s hypothesis that the average height is different according to the number of
complaints using all 7 steps of a hypothesis.
Data
Few
6.2
5.8
Average 6.00
Std dev 0.283
Some
5.9
6.1
5.9
5.5
5.85
0.251
Overall average: 5.77
P-value = 0.3845
Many
5.1
5.4
6.1
 6.2  5.77    5.8  5.77    5.9  5.77  
2
2
2
 6.1  5.77    5.9  5.77    5.5  5.77  
2
2
2
 5.1  5.77    5.4  5.77    6.1  5.77  
2
2
2
1.096
5.53
0.513
 2  1 0.283   4  1 0.251   3  1 0.513
2
2
2

0.796
15. An experiment was run to compare four types of metal plating on the resistance of a sword to
oxidization. The sample sizes were 25, 15, 181 and 22, the means were 50, 55, 48, 53, and the
corresponding estimated standard deviations were 17, 24, 8 and 19. The overall average was
49, and the total sample size was 243. Test if metal plating changes the resistance assuming the
p-value is 0 and the data is normal with equal variances. The following equations may or may
not be helpful:
2550  49  1555  49  18148  49  2253  49  1098
2
2
2
2
25  117 2  15  1242  181  182  22  1192  34101
25  172  50  552  22  192  48  532  123
16. There are three companies (A, B, and C) trying to bid for construction of a preschool. The
preschool is worried about getting a bad company. They randomly select months (3 from
company A, 4 from company B, and 5 from company C) and find the number of complaints the
company had for those months. The data is shown below. Test with 5% significance whether it
matters which company they choose (Assume normality and equal variances. Use all 7 steps of
a hypothesis. As a hint, the p-value is 0.10)
Company A: 0, 19, 38
Company B: 0, 16, 24, 48
Company C: 16, 39, 64, 68, 68