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Statistics – Sample 1


Researchers are conducting a state-wide survey for the U.S. Postal Service. The survey records many different variables of interest.  Which of the following variables is categorical?
A) County of residence.
B) Number of people, both adults and children, living in the household.
C) Total household income, before taxes, in 2010.
D) Age of respondent.


Answer – A


When examining a distribution of a quantitative variable, which of the following features do we look for?
A) Overall shape, center, and spread.
B) Symmetry or skewness.
C) Deviations from overall patterns such as outliers.
D) The number of peaks or modes.
E) All of the above.Answer – E


According to the American Cancer Society, the decline in colorectal cancer mortality, primarily attributed to early detection and treatment, have not been consistent among race/ethnic groups.  A colorectal exam is one method for early detection of colorectal cancer. In 2008, 29.5% of Whites, 56.9% of African Americans, and 62.4% of Hispanics had not received a colorectal exam within the last ten years. What is the best method to display these data?
A) Histogram
B) Pie chart
C) Bar graph
D) Stem-and-leaf plotAnswer – B



A researcher reports that, on average, the participants in his study lost 10.4 lbs after two months on his new diet.  A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report must be a fraud.  Which of the following statements is correct?
A) Your friend must not have followed the diet correctly because she did not lose weight.
B) Because your friend did not lose weight, the report must not be correct.
C) The report gives only the average.  This does not imply that all participants in the study lost 10.4 lbs or even that all participants lost weight.  Your friend’s experience does not necessarily contradict the study results.
D) In order for the study to be correct, we must now add your friend’s results to those of the study and re-compute the new average.Answer – B


A sample of 16 people is taken, and their weights are measured. The standard deviation of these 16 measurements is computed to be 5.4.  What is the variance of these measurements?
A) 2.24 lbs
B) 2.24 lbs2
C) 29.16 lbs
D) 29.16 lbs2


Answer – D


The standard deviation s is a useful measure of a characteristic of a distribution of data values.  Which of the following statements about s is FALSE?
A) The standard deviation measures the spread of the data around the mean.
B) The standard deviation is appropriate as a measure of spread when the mean is chosen as the measure of center.
C) The standard deviation can never be zero.
D) The standard deviation is not resistant; a few outliers can make s very large.
E) As the data values become more spread out about their mean, s becomes larger.

Answer – C



Problem 7


Research Question: What is the average daily number of hours of sleep over a one year period?


Sample: Hours of sleep for 100 randomly selected students the night before an exam.

Population: All students in the university.


a.         Representative

b.         Not representative

Answer – B


Problem 8


For a survey of American diets a random sample of 1000 people were contacted. Of the 1000 people, 340 people completed the questionnaire. The results of this study, if applied to all Americans, are questionable because of

a.         a large margin of error.

b.         selection bias.

c.         nonresponse bias.

d.         response bias.

Answer – C


Problem 9

Which one of the following statements is true about sample size and margin of error?

a.         Increasing the sample size of a survey decreases the margin of error.

b.         Increasing the sample size of a survey increases the margin of error.

c.         Increasing the sample size of a survey does not change the margin of error.

d.         Increasing the sample size of a survey only changes the margin of error if there is an error (a mistake) in the way the survey is conducted.

Answer – A



Problem 10

A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. An approximate 95% confidence interval for the proportion of all 18-24 year olds who believe that their health is extremely important is

a.         between 41% and 61%.

b.         between 46% and 56%.

c.         between 48% and 54%.

d.         between 50% and 52%.

Answer – C



Problem 11


A list of 5 pulse rates is: 70, 64, 80, 74, 92. What is the median for this list?

a.         74

b.         76

c.         77

d.         80

Answer – A


Problem 12


One hundred adults who had either Type 1 or Type 2 diabetes were randomly divided into 2 groups to determine if the inhalable version of insulin is able to manage blood sugar levels just as well as injected insulin.

a.         Observational Study

b.         Experiment

Answer – B



Use the following to answer questions 13-14:


Many residents of suburban neighborhoods own more than one car but consider one of their cars to be the main family vehicle. The age of these family vehicles can be modeled by a Normal distribution with a mean of 2 years and a standard deviation of 6 months.



What percentage of family vehicles is between 1 and 3 years old?
A) Cannot be determined based on the information given.
B) 68%
C) 95%
D) 99.7%Answer – C



What is the standardized value for a family vehicle that is 3 years and 3 months old?
A) 0.22
B) 2.5
C) 2.6
D) 2.92Answer – B



Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z < 1.1?
A) 0.1357
B) 0.2704
C) 0.8413
D) 0.8643Answer – D




Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to –0.5 < Z < 1.2?
A) 0.3085
B) 0.8849
C) 0.5764
D) 0.2815

Answer – D


The variable Z has a standard Normal distribution. Find the value z such that 85% of the observations fall below z.
A) z = –1.04
B) z = 0.80
C) z = 0.85
D) z = 1.04Answer – D








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