50 multiple questions for statistics and probability
QUESTION 1
Suppose the American Medical Association Center for Health Policy Research included data, by state, on the number of community hospitals and the average patient stay (in days) in its publication. The data (by state) are shown in the table.
Which two states have an unusually high number of hospitals?
State 
Hospitals 
State 
Hospitals 
State 
Hospitals 

Alabama 
330 
Colorado 
72 
Georgia 
163 

Alaska 
16 
Connecticut 
35 
Hawaii 
19 

Arizona 
61 
Delaware 
8 
Idaho 
41 

Arkansas 
88 
Dist. of Columbia 
11 
Illinois 
279 

California 
236 
Florida 
289 
Indiana 
113 

Iowa 
123 
Nebraska 
90 
Rhode Island 
12 

Kansas 
133 
Nebraska 
21 
S.Carolina 
68 

Kentucky 
107 
New Hampshire 
21 
S.Dakota 
52 

Louisiana 
459 
New Jersey 
96 
Tennessee 
122 

Maine 
38 
New Mexico 
37 
Texas 
235 

Maryland 
51 
New York 
333 
Utah 
42 

Mass. 
101 
N.Caroline 
117 
Vermont 
15 

Michigan 
175 
N.Dakota 
47 
Virginia 
98 

Minnesota 
276 
Ohio 
193 
Washington 
92 

Mississippi 
102 
Oklahoma 
399 
W.Virginia 
59 

Missouri 
133 
Oregon 
66 
Wisconsin 
478 

Montana 
53 
Pennsylvania 
231 
Wyoming 
27 


a. 
Florida and Wisconsin 



b. 
Alabama and Arkansas 



c. 
Wisconsin and Louisiana 



d. 
Maine and Iowa 



e. 
none of these choices 


4 points
QUESTION 2
In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 2.0. Suppose you are going to dig up and examine 40 liters of sediment at this site. Let r = 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your 40 liters of sediment. Find the probability that you will find 1 or more artifacts in the 40 liters of sediment. Round your answer to the nearest ten thousandth.

a. 
0.0137 

b. 
0.0027 

c. 
0.0013 

d. 
0.0096 

e. 
0.0107 
4 points
QUESTION 3
Compute the population standard deviation σ for the following sample data, assuming the sample comprises the entire population. Round your answer to the nearest hundredth.
x: 
21 
19 
12 
30 
29 


a. 
9.71 



b. 
7.46 



c. 
8.68 



d. 
6.68 



e. 
2.29 

4 points
QUESTION 4
What is a sampling distribution?

a. 
A set of measurements (or counts), either existing or conceptual 

b. 
A numerical descriptive measure of a sample 

c. 
A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability 

d. 
A probability distribution for a sample statistic 

e. 
A numerical descriptive measure of a population 
4 points
QUESTION 5
To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:
Twin Pair 
1 
2 
3 
4 
5 
6 
School A 
80 
145 
118 
90 
112 
118 
School B 
83 
135 
115 
105 
105 
113 
Twin Pair 
7 
8 
9 
10 
11 
12 
School A 
98 
112 
115 
144 
124 
96 
School B 
93 
87 
98 
132 
135 
105 
Suppose a sign test for matched pairs with a 5% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school A. Calculate the Pvalue. Round your answer to four decimal places.

a. 
0.3001 

b. 
0.2501 

c. 
0.1251 

d. 
0.7499 

e. 
0.3071 
4 points
QUESTION 6
A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales.
Person 
1 
2 
3 
4 
5 
6 
x rank 
8 
11 
2 
4 
5 
3 
y rank 
7 
2 
3 
6 
5 
8 
Person 
7 
8 
9 
10 
11 
x rank 
7 
9 
10 
1 
6 
y rank 
9 
11 
10 
1 
4 
Using a 10% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). What is the level of significance α?

a. 
a = 0.10 

b. 
a = 0.03 

c. 
a = 0.05 

d. 
a = 1.00 

e. 
a = 10.00 
4 points
QUESTION 7
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth.
x: 
11 
0 
36 
22 
34 
24 
25 
11 
11 
22 

y: 
9 
3 
28 
14 
23 
16 
14 
3 
4 
9 


a. 
X = 37.0 and y = 12.0 



b. 
X = 65.0 and y = 9.1 



c. 
X = 10.8 and y = 8.5 



d. 
X = 152.0 and y = 9.8 



e. 
X = 8.5 and y = 10.8 


4 points
QUESTION 8
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 247 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.1. Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis?

a. 
The Pvalue is less than the level of significance so the data are statistically significant. Thus, we reject the null hypothesis. 

b. 
The Pvalue is less than the level of significance so the data are not statistically significant. Thus, we reject the null hypothesis. 

c. 
The Pvalue is less than the level of significance so the data are statistically significant. Thus, we fail to reject the null hypothesis. 

d. 
The Pvalue is greater than the level of significance so the data are not statistically significant. Thus, we reject the null hypothesis. 

e. 
The Pvalue is less than the level of significance so the data are statistically significant. Thus, we reject the null hypothesis. 
4 points
QUESTION 9
Suppose the age distribution of the Canadian population and the age distribution of a random sample of 528 residents in the Indian community of Red Lake are shown below.


Observed Number 
Age (years) 
Percent of Canadian Population 
in Red Lake Village 
Under 5 
6.4% 
38 
5 to 14 
11.8% 
48 
15 to 64 
70.3% 
397 
65 and older 
11.5% 
45 
Use a = 0.05 to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Given a value of 9.673 for x^{2}, find (or estimate) the Pvalue of the sample test statistic.

a. 
0.01 < PValue < 0.025 

b. 
PValue < 0.005 

c. 
0.025 < PValue < 0.05 

d. 
0.25 < PValue < 0.50 

e. 
0.05 < PValue < 0.10 
4 points
QUESTION 10
Identify the level of measurement corresponding to the data "Cost of rod and reel" associated with fishing.

a. 
interval 

b. 
nominal 

c. 
ratio 

d. 
none of these choices 

e. 
ordinal 
4 points
QUESTION 11
Data may be classified by one of the four levels of measurement. What is the name of the lowest level?

a. 
nominal 

b. 
ratio 

c. 
ordinal 

d. 
interval 

e. 
simple 
4 points
QUESTION 12
Compute the expected age μ of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.
Age range (yr) 
20–29 
30–39 
40–49 
50–59 
60–69 
70–79 
80+ 

Midpoint (x) 
24.5 
34.5 
44.5 
54.5 
64.5 
75.5 
84.5 

Percent of nurses 
5.7% 
9.6% 
19.5% 
29.1% 
24.9% 
9.0% 
2.2% 


a. 
53.93 



b. 
59.50 



c. 
43.96 



d. 
54.50 



e. 
53.96 


4 points
QUESTION 13
Wetlands offer a diversity of benefits. They provide habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years the United States has lost more than half its wetlands. Suppose Environmental Almanac gives the percentage of wet lands lost in each state in the last 200 years. Assume that for the lower 48 states, the percentage loss of wetlands per state is as follows:
46 
37 
36 
42 
81 
20 
73 
59 
35 
50 
87 
52 
24 
27 
38 
56 
39 
74 
56 
31 
27 
91 
46 
9 
54 
52 
30 
33 
28 
35 
35 
23 
90 
72 
85 
42 
59 
50 
49 

48 
38 
60 
46 
87 
50 
89 
49 
67 

The distribution is approximately mound shaped.

a. 
True 

b. 
False 
4 points
QUESTION 14
1. Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 56% of all Wing Foot stores show a profit the first year; 75% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 80% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(A and B), if P(A) = 0.56, P(B) = 0.75 and P(BA) = 0.80. Round your answer to the nearest hundredth.

a. 
0.80 

b. 
0.51 

c. 
0.70 

d. 
0.45 

e. 
0.94 
4 points
QUESTION 15
1. How hot does it get in Death Valley? Assume that the following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures^{o}F were taken from May to November in the vicinity of Furnace Creek. Compute the median for these ground temperatures. Round your answer to the nearest tenth.
148 
151 
168 
173 
194 
178 
193 

194 
178 
178 
168 
163 
151 
144 


a. 
170.5 



b. 
193.5 



c. 
341.0 



d. 
168.0 



e. 
159.5 

4 points
QUESTION 16
Assume that the following data represent baseball batting averages (multiplied by 1000) for a random sample of National League players near the end of the baseball season. The frequency table showing class limits, class boundaries, midpoints and frequency is given below. Draw a histogram.

Boundaries 
Midpoint 
Frequency 






4 points
QUESTION 17
1. There are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.
r 
p(r) 
0 
0.041 
1 
0.200 
2 
0.368 
3 
0.300 
4 
0.092 
4 points
QUESTION 18
1. Richard has been given a 9question multiplechoice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. What is the value of p? (p is the value of success) Round your answer to the nearest tenth.

a. 
0.3 

b. 
9.0 

c. 
3.0 

d. 
2.7 

e. 
27.0 
4 points
QUESTION 19
In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information.
x 
0.251 
0.259 
0.29 
0.265 
0.269 
y 
1.3 
3.7 
5.8 
3.9 
3.7 
Make a scatter diagram for the data. Draw the line that best fits the data.
4 points
QUESTION 20
Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.
33.7 
26.9 
31.2 
27.0 
33.1 
27.7 
34.0 
24.7 
33.7 
32.8 
25.8 
28.8 






Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. The number of runs is 10. What is the lower critical number c_{1}?

a. 
1 

b. 
4 

c. 
2 

d. 
5 

e. 
3 
4 points
QUESTION 21
The probability of a single radar station detecting an enemy plane is 0.75 and the probability of not detecting an enemy plane is 0.25. How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

a. 
2 

b. 
none of these choices 

c. 
3 

d. 
4 

e. 
1 
4 points
QUESTION 22
A professional employee in a large corporation receives an average of μ = 42.7 emails per day. Most of these emails are from other employees in the company. Because of the large number of emails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an email. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of x = 35.3 emails per day. The computer server through which the emails are routed showed that σ = 19.6. Has the new policy had any effect? Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of emails received per day per employee. What is the value of the test statistic?

a. 
–0.061 

b. 
0.378 

c. 
–2.327 

d. 
0.061 

e. 
2.327 
4 points
QUESTION 23
What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Find the probability that a British nurse selected at random in 1851 would be 70 years of age or older. Round your answer to nearest thousandth.
Age range (yr) 
20–29 
30–39 
40–49 
50–59 
60–69 
70–79 
80+ 

Midpoint (x) 
24.5 
34.5 
44.5 
54.5 
64.5 
75.5 
84.5 

Percent of nurses 
5.7% 
9.7% 
19.5% 
29.2% 
25.0% 
9.1% 
1.8% 


a. 
0.091 



b. 
0 



c. 
0.099 



d. 
0.105 



e. 
0.109 


4 points
QUESTION 24
Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are moundshaped and symmetric for these two regions.
Region I: ;
981 726 686 496 657 627 815 504 950 605 570 520
Region II: ;
1024 830 526 502 539 373 888 685 868 1093 1132 792 1081 722 1092 844
Let be the population mean and be the population standard deviation for . Let be the population mean and be the population standard deviation for . Determine and examine the 90% confidence interval for . Does the interval consist of numbers that are all positive? all negative? or different signs? At the 90% level of confidence, is one region more interesting that the other from a geochemical perspective?

a. 
The interval contains both positive and negative numbers. We can say at the required confidence level that one region is more interesting than the other. 

b. 
The interval contains only positive numbers. We can say at the required confidence level that one region is more interesting than the other. 

c. 
The interval contains only negative numbers. We cannot say at the required confidence level that one region is more interesting than the other. 

d. 
The interval contains only positive numbers. We cannot say at the required confidence level that one region is more interesting than the other. 

e. 
The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other. 
4 points
QUESTION 25
When do creative people get their good ideas? Assume that the survey of 963 inventors gives the following information:
Time of Day When Good Ideas Occur 

Time 
Number of Inventors 
6 A.M. – 12 noon 
281 
12 noon – 6 P.M. 
120 
6 P.M. – 12 midnight 
320 
12 midnight – 6 A.M. 
242 
Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a good idea during the time interval from 6 A.M. to 12 noon. Write your answer as a fraction in simplest form.
4 points
QUESTION 26
The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x_{1}, x_{2}, and x_{3}, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals.
Descriptive Statistics 

Variable 
N 
Mean 
Median 
TrMean 
StDev 
SE Mean 
x_{1} 
15 
159.35 
159.65 
159.35 
3.401 
0.878134 
x_{2} 
15 
72.77 
73.77 
72.77 
1.722 
0.444618 
x_{3} 
15 
185.90 
185.20 
185.90 
4.266 
1.101476 
Variable 
Minimum 
Maximum 
Q1 
Q3 
x_{1} 
126 
173 
140.497 
166.049 
x_{2} 
45 
89 
47.721 
78.484 
x_{3} 
129 
249 
140.492 
222.010 
Correlations (Pearson) 


x_{1} 
x_{2} 
x_{2} 
0.848 

x_{3} 
0.817 
0.634 
Regression Analysis
The regression equation is
x_{1} = 0.703 + 1.388x_{2} + 0.907x_{3 }
Predictor 
Coef 
StDev 
T 
P 
Constant 
0.703 
0.495 
1.42 
0.091 
x_{2} 
1.388 
0.669 
2.07 
0.030 
x_{3} 
0.907 
0.390 
2.33 
0.019 
S = 0.424 
Rsq = 92.5 % 
Rsq(adj) = 91.1 % 


Test the coefficient of in the regression equation to determine if it is zero or not zero. Use a level of significance of 5%. Do you accept or reject the null hypothesis that the coefficient should equal zero?

a. 
accept 

b. 
reject 
4 points
QUESTION 27
How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the following information.
x 
4 
7 
14 
19 
21 
y 
50 
85 
130 
160 
175 
Make a scatter diagram for the data.4 points
QUESTION 28
Draw a tree diagram to display all the possible headtail sequences that can occur when you flip a coin foour times.

a. 


b. 


c. 


d. 


e. 
4 points
QUESTION 29
Suppose automobile insurance companies gave annual premiums for toprated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states.
Which state has the highest median premium?

a. 
Pennsylvania has the highest median premium. 

b. 
California has the highest median premium. 

c. 
Texas as well as California have the highest median premium. 

d. 
Texas has the highest median premium. 

e. 
none of these choices 
4 points
QUESTION 30
1. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution.
Age range (yr) 
20–29 
30–39 
40–49 
50–59 
60–69 
70–79 
80+ 
Midpoint (x) 
24.5 
34.5 
44.5 
54.5 
64.5 
75.5 
84.5 
Percent of nurses 
9.8% 
5.6% 
19.4% 
24.9% 
29.3% 
9.3% 
1.7% 
4 points
QUESTION 31
The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x_{1}, x_{2}, and x_{3}, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals.
Descriptive Statistics 

Variable 
N 
Mean 
Median 
TrMean 
StDev 
SE Mean 
x_{1} 
15 
155.56 
156.06 
155.56 
3.815 
0.985029 
x_{2} 
15 
63.42 
64.02 
63.42 
1.226 
0.316552 
x_{3} 
15 
195.04 
194.64 
195.04 
4.164 
1.075140 
Variable 
Minimum 
Maximum 
Q1 
Q3 
x_{1} 
126 
179 
144.445 
165.050 
x_{2} 
42 
83 
47.888 
77.461 
x_{3} 
120 
250 
139.698 
222.040 
Correlations (Pearson) 


x_{1} 
x_{2} 
x_{2} 
0.870 

x_{3} 
0.802 
0.517 
Regression Analysis
The regression equation is
x_{1} = 0.804 + 1.308x_{2} + 0.966x_{3 }
Predictor 
Coef 
StDev 
T 
P 
Constant 
0.804 
0.692 
1.16 
0.134 
x_{2} 
1.308 
0.732 
1.79 
0.050 
x_{3} 
0.966 
0.705 
1.37 
0.098 
S = 0.319 
Rsq = 90.6 % 
Rsq(adj) = 92.6 % 


Relative to its mean, which variable has the smallest spread of data values?
 X_{1}
 X_{2}
 X_{3}
4 points
QUESTION 32
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds):
4.28 
4.36 
4.43 
4.92 
5.16 
4.13 
2.52 
4.52 
4.50 
3.02 
2.55 
3.53 
4.75 
3.67 
3.20 
4.38 
For this plot, the sample variance is . Another random sample of years for a second plot gave the following annual wheat production (in pounds):
3.76 
3.94 
3.95 
3.80 
3.70 
3.74 
4.06 
3.94 
3.98 
4.04 
3.85 
3.94 
3.89 
4.05 
3.88 
4.04 
For this plot, the sample variance is . Test the claim using that the population variance of annual wheat production for the first plot is larger than that for the second plot.
What are the degrees of freedom?

a. 
14; 15 

b. 
15; 15 

c. 
14; 16 

d. 
15; 14 

e. 
16; 14 
4 points
QUESTION 33
A random sample of communities in western Kansas gave the following information for people under 25 years of age.
: Rate of hay fever per 1000 population for people under 25
A random sample of regions in western Kansas gave the following information for people over 50 years old.
: Rate of hay fever per 1000 population for people over 50
Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a = 0.05 State the null and alternate hypotheses.
4 points
QUESTION 34
Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States.

Less Than 1 Year 
1 – 2 Years 
3 – 4 Years 
5 – 9 Years 
10 – 14 Years 
15 or More Years 
Row Total 
East 
32 
54 
59 
112 
77 
118 
452 
Midwest 
31 
68 
68 
120 
63 
173 
523 
South 
53 
92 
93 
158 
106 
158 
660 
West 
41 
56 
67 
78 
45 
86 
373 
Column Total 
157 
270 
287 
468 
291 
535 
2008 
What is the probability that a customer chosen at random has been loyal 5 or more years given that he or she is from the South? Round your answer to the nearest thousandth.

a. 
0.210 

b. 
0.326 

c. 
0.639 

d. 
0.417 

e. 
none of these choices 
4 points
QUESTION 35
Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. What is the probability that from 45 to 47 of the claims have been padded?

a. 
0.167 

b. 
0.119 

c. 
0.104 

d. 
0.056 

e. 
0.222 
4 points
QUESTION 36
What percentage of the general U.S. population have bachelor’s degrees? Suppose that the Statistical Abstract of the United States, 120th Edition, gives the following percentage of bachelor’s degrees by state. For convenience, the data are sorted in increasing order.
17 
18 
18 
18 
19 
20 
20 
20 
21 
21 
21 
21 
21 
22 
22 
22 
22 
22 
23 
23 
24 
24 
24 
24 
24 
25 
25 
25 
25 
26 
26 
26 
26 
26 
26 
27 
27 
27 
28 
28 
28 
29 
29 
31 
31 
32 
32 
34 
35 
38 
Illinois has a bachelor’s degree percentage rate of about 18%. Into what quartile does this rate fall?

a. 
second quartile 

b. 
first quartile 

c. 
third quartile 

d. 
first quartile as well as second quartile 

e. 
none of these choices 
4 points
QUESTION 37
Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 61% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute if , , and . Round your answer to the nearest hundredth.

a. 
0.46 

b. 
0.44 

c. 
0.76 

d. 
0.80 

e. 
0.87 
4 points
QUESTION 38
How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. Assume that a sample of 32 cowboys gave the following years of longevity:
59 
52 
67 
86 
72 
66 
99 
89 
84 
91 
91 
92 
69 
68 
87 
86 
73 
61 
71 
75 
72 
73 
85 
84 
91 
57 
77 
76 
84 
93 
58 
49 

Make a stemandleaf display for these data.

a. 
4 9 = 49 years 

b. 
4 9 = 49 years 

c. 
4 9 = 49 years 

d. 
4 9 = 49 years 

e. 
none of these choices 
4 points
QUESTION 39
Wind Mountain is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic blackonwhite. At three different sites the number of such sherds was counted in local dwelling excavations.
Site I 
Site II 
Site III 
51 
34 
18 
46 
46 
22 
57 
53 
44 
44 
59 
23 
18 

61 
33 

40 
15 


Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic blackonwhite sherd counts for the three sites? Test given a = 0.01.
Find (or estimate) the Pvalue of the sample test statistic.

a. 
PValue = 0.01 

b. 
0.05 < PValue < 0.1 

c. 
PValue = 0.05 

d. 
PValue > 0.1 

e. 
0.01 < PValue < 0.05 
4 points
QUESTION 40
Jim has a 5yearold car in reasonably good condition. He wants to take out a $50,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:
x = age 
5 
6 
7 
8 
9 
P(accident) 
0.01182 
0.01282 
0.01386 
0.01513 
0.01602 
Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $50,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years? Round your answers to the nearest dollar.

a. 
$591, $641, $693, $747, $801 

b. 
$591, $646, $693, $747, $801 

c. 
$591, $641, $693, $757, $801 

d. 
$581, $641, $693, $747, $801 

e. 
$581, $646, $693, $757, $801 
4 points
QUESTION 41
Finish times (to the nearest hour) for 57 dogsled teams are shown below. Use five classes. Categorize the basic distribution shape as uniform, moundshaped symmetric, bimodal, skewed left, or skewed right.
The relative frequency histogram of the above data is given below.

a. 
Bimodal 

b. 
none of these choices 

c. 
moundshaped symmetric 

d. 
approximately moundshaped symmetric 

e. 
Skewed right 
4 points
QUESTION 42
Does talking while walking slow you down? Suppose a study considered mean cadence (steps per minute) for subjects using no walking device, a standard walker, and a rolling walker. In addition, the cadence was measured when the subjects had to perform dual tasks. The second task was to respond vocally to a signal or respond to an interview question while walking. Cadence was measured for subjects who were just walking (using no walking device, a standard walker, or a rolling walker), for subjects required to respond to a signal, and for subjects required to respond to an interview question while walking. How many cells are there in the data table?

a. 
9 

b. 
8 

c. 
7 

d. 
12 

e. 
1 
4 points
QUESTION 43
John runs a computer software store. He counted 125 people who walked by his store in a day, 51 of whom came into the store. Of the 51, only 23 bought something in the store. Estimate the probability that a person who comes into the store will buy nothing. Round your answer to the nearest hundredth.

a. 
0.82 

b. 
0.59 

c. 
0.22 

d. 
0.55 

e. 
none of these choices 
4 points
QUESTION 44
Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (–) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 137 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Condition Present 
Condition Absent 
Row Total 
Test Result + 
119 
18 
137 
Test Result – 
18 
46 
64 
Column Total 
137 
64 
201 
Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result – or condition present). Round your answer to the nearest hundredth.

a. 
0.91 

b. 
0.28 

c. 
0.09 

d. 
0.13 

e. 
none of these choices 
4 points
QUESTION 45
1. Suppose a certain species bird has an average weight of x = 3.80 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with o = 0.37 grams. For a small group of 10 birds, find the margin of error for a 70% confidence interval for the average weights of these birds.

a. 
0.06 grams 

b. 
0.02 grams 

c. 
1.04 grams 

d. 
0.12 grams 

e. 
0.04 grams 
4 points
QUESTION 46
Finish times (to the nearest hour) for 57 dogsled teams are shown below. Draw a relative – frequency histogram. Use five classes.
261 
270 
236 
244 
280 
296 
284 
298 
289 
289 
248 
256 

338 
360 
341 
333 
261 
267 
287 
296 
313 
311 
309 
309 

299 
303 
277 
283 
304 
305 
288 
290 
288 
289 
297 
299 

332 
330 
309 
328 
309 
328 
285 
291 
295 
298 
306 
315 

310 
318 
318 
320 
333 
321 
323 
324 
327 





























4 points
QUESTION 47
In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was . Suppose you are going to dig up and examine liters of sediment at this site. Let 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your liters of sediment. Find the probability that you will find fewer than prehistoric artifacts in the liters of sediment. Round your answer to the nearest ten thousandth.
4 points
QUESTION 48
1. A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?

a. 
3/4 

b. 
0 

c. 
1/4 

d. 
1/2 

e. 
1 
4 points
QUESTION 49
1. If event A is certain to occur, what is P(A)?

a. 
0.5 

b. 
0.25 

c. 
0.75 

d. 
1 

e. 
0 
4 points
QUESTION 50
1. It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:
x 
5.50 
6.50 
7.50 
7.75 
8.75 
y 
15 
32 
55 
39 
72 
2.
Find a for the equation of the leastsquares line y = a + bx.

a. 
75.923 

b. 
42.698 

c. 
–75.923 

d. 
–42.698 

e. 
–42.068 
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