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Final You scored 50 out of 50
Question 1 Your answer is CORRECT.
Suppose that in a large metropolitan area, 79% of all households have cable tv. Suppose you are interested in
selecting a group of six households from this area. Let X be the number of households in a group of six
households from this area that have cable tv. For what proportion of groups will at most two of the
households have cable tv? a) 0.020 b) 0.980 c) 0.091 d) 0.888 e) 0.112 > pbinom(2,6,0.79)
[1] 0.02022797 Question 2 Your answer is CORRECT.
A potato chip company calculated that there is a mean of 75.2 broken potato chips in each production run
with a standard deviation of 5.4. If the distribution is approximately normal, find the probability that there
will be fewer than 67 broken chips in a run.
a) 0.364 b) 0.064 c) 0.314 d) 0.032 e) 0.936 > pnorm(67,75.2,5.4)
[1] 0.06444187 Question 3 Your answer is CORRECT.
A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc) is:
0
1
2
3
4 0.09 0.19 0.21 0.32 0.19 Find the mean and variance for the grades in this class. a) mean = 2.33, variance = 1.5211 b) mean = 2.42, variance = 0.76055 c) mean = 2.33, variance = 0.76055 d) mean = 2.24, variance = 1.2333 e) mean = 2.24, variance = 1.5211 > x=c(0,1,2,3,4)
> px=c(0.09,0.19,0.21,0.32,0.19)
mean =
> sum(x*(px))
[1] 2.33
var =
> sum((x^2)*px)-2.33^2
[1] 1.5211 Question 4 Your answer is CORRECT.
The weights of male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a) The median weight of the male students is about 166 lbs. b) About 50% of the male students have weights between 150 and 185 lbs. c) The mean weight of the female students is about 120 because of symmetry. d) The male students have less variability than the female students. Question 5 Your answer is CORRECT.
Given that a) 0.696 b) 0.304 c) 0.857 , find P(A | B) = P(A and B)/P(B)
= 0.14/0.46
=0.3043478 . d) 0.452 e) 0.143 Question 6 Your answer is CORRECT.
Identify the most appropriate test to use for the following situation:
A national computer retailer believes that the average sales are greater for salespersons with a college
degree. A random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year,
while 17 salespersons without a college degree averaged $3301 in weekly sales. The standard deviations
were $468 and $642 respectively. Is there evidence to support the retailer's belief? a) Two sample z test for means b) Two sample z test for proportions c) Two sample t test for means d) One sample z test for proportions e) One sample t test for means f) Matched pairs t test for means g) One sample z test for means H0 : mean(college) = mean(nocollege),
Ha : mean(college) > mean (nocollege)
t = (3542-3301)/sqrt(((468^2)/14)+((642^2)/17)) Question 7 Your answer is CORRECT.
A random sample of 169 cans of fruit nectar is drawn from among all cans produced in a run. Prior
experience has shown that the distribution of the contents has a mean of 14.11 ounces and a standard
deviation of 2.18 ounce. What is the probability that the average contents of the 169 sample cans is less than
13.74 ounces?
a) 0.973 n = 169, pop.mean = 14.11, pop.sd = 2.18 b) 0.014 c) 0.034 P(x<13.74) =
> pnorm(13.74,14.11,2.18/sqrt(169))
[1] 0.01367723 d) 0.027 e) 0.986 Question 8 Your answer is CORRECT.
A random variable X has a probability distribution as follows: X 0 1 2 3 4 P(X) 4k 3k 2k 4k 2k What is P(X < 3)?
a) 4k+3k+2k+4k+2k = 1
15k = 1
k = 1/15 b) P(X<3) =
4/15 + 3/15 + 2/15 = 9/15 = 3/5 c) d) e) Cannot be determined. Question 9 Your answer is CORRECT.
Find a value of so that . a) > qnorm(0.66)
[1] 0.4124631 b) c) d) e) Question 10 Your answer is CORRECT.
The following table displays the results of a sample of 100 in which the subjects indicated their favorite ice
cream of three listed. The data are organized by favorite ice cream and age group. What is the probability
that a person chosen at random will be between 20 and 40 years old if he or she favors vanilla? Age Chocolate Vanilla Strawberry Over 40 12 9 9 2040 13 9 13 Under 20 9 16 34
a) 10 b) c) d) e) Question 11 Your answer is CORRECT.
A random sample of 144 observations produced a sample proportion of 0.35. An approximate 90%
confidence interval for the population proportion p is between
a) 0.285 and 0.415 b) 0.285 and 0.428 c) 0.310 and 0.390 d) 0.272 and 0.428 e) 0.269 and 0.431 > 0.35+c(-1,1)*qt(1.9/2,143)*sqrt(0.35*0.65/144)
[1] 0.2841949 0.4158051 Question 12 Your answer is CORRECT.
Data for gas mileage (in mpg) for different vehicles was entered into a software package and part of the
ANOVA table is shown below: Source DF SS MS Vehicle 5 Error 6 Total
Determine the pvalue for the data. a) 0.0106 b) 0.0318 c) 0.0539 d) 0.5050 550 275.00 306 51.00 11 856 F = MSTr/MSE
> 275/51
[1] 5.392157
P(F) =
> 1-pf(5.392157,5,6)
[1] 0.03178149 e) 0.0159 Question 13 Your answer is CORRECT.
If the Pvalue is larger than the level of significance α, then the researcher should __________ at level α.
a) Fail to reject H0 b) Reject H0 c) Accept H0 Question 14 Your answer is CORRECT.
The onesample t statistic for a test of H0: μ = 13 vs. Ha: μ < 13 based on n = 17 observations has the test
statistic value of t = −1.45. What is the pvalue for this test?
a) 0.083 b) 0.383 c) 0.166 d) 0.917 e) 0.000 > pt(-1.45,16)
[1] 0.0831891 Question 15 Your answer is CORRECT.
This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A
proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1582
A study of iron deficiency in infants compared samples of infants whose mothers chose different ways of
feeding them. One group contained breastfed infants. The children in another group were fed a standard
baby formula without any iron supplements. Her are summary results on blood hemoglobin levels at 12
months of age:
> 1-pt(3.633862,23)
Group
n
x
s
[1] 0.0006948736
H0 : mean(F) = mean(B),
RH0
Breastfed 24 15.2 2.2 We have significant evidence
Ha : mean(F) > mean(B)
Formula 32 17.2 1.8 that the mean hemoglobin level
df = 24-1 = 23
t = (17.2-15.2)/sqrt(((1.8^2)/32)+((2.2^2)/24)) is greater among formula-fed
babies.
t= 3.633862
Part a: We want to see if the mean hemoglobin level is greater among formulafed babies. State the
hypotheses and perform the significance test on your hypothesis. Report the test statistic and pvalue. State your conclusion in terms of the issue.
Part b: Give a 95% confidence interval for the mean difference in hemoglobin level between the two
populations ofinfants. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 16 Your answer is CORRECT.
This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A
proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1671
Consumer Reports rated 77 cereals on a scale of 0 to 100. The number of grams of sugar contained in each
serving of the corresponding cereals was also recorded. Using sugar as the explanatory variable and the
Consumer Reports rating as the dependent variable, computer output of the data is as follows (the pvalues
are intentionally left blank): Predictor Coef StDev T P part b
CI : -2.41 +/- qt(1.95/2,76)*0.24
> -2.41+c(-1,1)*qt(1.95/2,76)*0.24
[1] -2.888001 -1.931999 Constant 59.28 1.948 30.43 Sugars − 2.41 0.24 − 10.12 part c S = 9.146 RSq = 57.7% RSq(adj) = 57.1% H0 : B = 0, Ha : B ≠ 0
t = -10.12
> 2*pt(-10.12,76)
[1] 9.844164e-16
Part a: What is the regression equation? ŷ = 59.28 - 2.41x
Part b: Calculate the 95% confidence interval of the slope of the regression line for all cereals. Part c: Use the information provided to test whether there is a significant relationship between the sugar
content and the Consumer Report rating at the 5% level. RH0
We have extremely strong
evidence that there is no sig.
a) I have placed my work and my answer on my answer sheet.
relationship between sugar content.
b) I want to have points deducted from my test for not working this problem. Question 17 Your answer is CORRECT.
This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A
proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1771
Suppose the random variable has CDF given by the function Part a: Find . = (1^4)/16 = 1/16
Part b: Find . = (1/16) - ((0.5^4)/16) = 0.05859375
Part c: Find the desity function . f(x) = (x^3)/4
0≤x≤2
0
otherwise
a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 18 Your answer is CORRECT.
This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A
proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1881
Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical
probabilities for each roll should be:
1
2
3
4
5
6 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % You roll the die 84 times and come up with the following distribution:
1 2 3 4 5 6 12 11 20 13 15 13 Part a: What type of test should be used in this situation? X^2 goodness of fit
Part b: State the hypothesis. H0 : The distribution is the same., Ha : The distribution is not the same.
Part c: What is the test statistic? Chi-squared test for given
Part d: Find the value and state your conclusion. > x=c(12,11,20,13,15,13)
> px=c(1/6,1/6,1/6,1/6,1/6,1/6) probabilities
data: x
> chisq.test(x,p=px)
X-squared = 3.7143, df = 5,
a) I have placed my work and my answer on my answer sheet.
p-value = 0.5912
FRH0
b) I want to have points deducted from my test for not working this problem. We have no evidence that
the distribution is not the
same.
Question 19 Your answer is CORRECT.
This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A
proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1984
The following data are for intelligencetest (IT) scores, reading rates (RR), and gradepoint averages (GPA)
of 8 atrisk students.
> GPA=c(3.0,2.0,1.7,2.5,2.0,2.7,
IT 155 206 156 172 209 191 163 207 2.6,1.8)
RR 43 33 27 35 25 36 36 26 > RR=c(43,33,27,35,25,36,36,26)
> IT=c(155,206,156,172,209,191,
GPA 3.0 2.0 1.7 2.5 2.0 2.7 2.6 1.8
163,207)
Part a: Calculate the line of best fit that predicts the GPA on the basis of RR scores.
Part b: Calculate the line of best fit that predicts the GPA on the basis of IT scores.
Part c: Which of the two lines calculated in parts a and b best fits the data? Justify your answer. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. part a :
> summary(lm(GPA~RR))
ŷ = -0.004863 + 0.070264x
R^2 = 0.8493
p-vlaue = 0.001135 part b :
> summary(lm(GPA~IT))
ŷ = 3.942032 - 0.009072x
R^2 = 0.2033
p-value = 0.2621 part c :
Line of part a fits best with the data.
R^2 for part a is higher at 0.8493 meaning that 84.93%
of the distribution can be explained by the equation/line.
P-value of part a tells us to reject the H0, thus saying
that RR scores are good at predicting GPA. ...

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