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# Descriptive statistics: 18 multiple choice questions

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Assignment: Week 1 Ch 1

1. A quality-control manager randomly selects 90 bottles of vinegar that were filled on September 21 to assess the calibration of the filling machine.
What is the population in the study?
A. Bottles of vinegar produced in the plant.
B. Bottles of vinegar produced in the plant on September 21.
C. The 90 bottles of vinegar produced in the plant on September 21.
D. The 90 bottles of vinegar produced in the plant.

What is the sample in the study?
A. The 90 bottles of vinegar produced in the plant in September.
B. Bottles of vinegar produced in the plant on September 21.
C. Bottles of vinegar produced in the plant.
D. The 90 bottles of vinegar in the plant on Sept. 21.

2. Determine whether the numerical value is a parameter or a statistic. Explain your reasoning.
A Survey of 42 out of hundreds in a dining hall showed that 17 enjoyed their meal.
A. Statistic, because the data set of all people in the dining hall is a sample.
B. Parameter, because the data set of all people in the dining hall is a sample.
C. Parameter, because the data set of 42 people in a dining hall is a sample.
D. Statistic, because the data of 42 people in a dining hall is a sample.
E. Parameter, because the data set of all people in the dining hall is a population.
F. Statistic, because the data set of all people in the dining hall is a population.
G. Statistic, because the data set of 42 people in a dining hall is a population.
H. Parameter, because the data set of 42 people in a dining hall is a population.

3. Suppose a survey of 558 women in the United States found that more than 605 are the primary investor in their household. Which part of the survey represents the descriptive branch of statistic?
Make an inference based on the results of the Survey.
Choose the best statement of the descriptive statistic in the problem.

A. There is an association between the 558 women and being the primary investor in their household.
B. 538 women were surveyed
C. 60% of women in the sample are the primary investor in their household.
D. There is an association between the 538 women and being the primary investor in their household.

Choose the best inference from the given information.
A. 538 women were surveyed.
B. 60% of women in the sample are the primary investor in their household.
C. There is an association between the 538 women and being the primary investor in their household.
D. There is as association between U.S. women and being the primary investor in their household

4. A study shows that students in first grade are shorter than students in fourth grade.
(a) Make an inference based on the results of the study. Choose the correct answer below.
(b) What might this inference incorrectly imply?
A. Students in first grade have not taken enough vitamins to grow yet.
B. Students in first grade are younger than the students in fourth grade and have grown less.
C. Students in fourth grade are shorter than students in first grade.
D. Students in first grade are shorter than students in fourth grade.

(c) What might this inference imply?
A. This inference may incorrectly imply that if you switched to fourth grade, you would be shorter than you would be if you were in the first grade.
B. This inference may incorrectly imply that students in first grade have not taken enough vitamins to grow yet.
C. This inference may incorrectly imply that students in first grade are younger than the students in fourth grade and have grown less.
D. This inference may incorrectly imply that if you switched to the first grade, you would be shorter than you would be if you were in the fourth grade.

5. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A population is the collection of some outcomes, responses, measurements, or counts that are of interest.
A. True.
B. False. A population is the collection of all outcomes, responses, measurements, or counts that are interest.
C. False. A sample is the collection of all outcomes, responses, measurements, or counts that are of interest.

6. Determine whether the variable is qualitative or quantitative.
Distance in miles to nearest outdoor stadium.
Is the variable qualitative or quantitative?
( ) Qualitative
( ) Quantitative

7. The following appear on a physician's intake form. Identify the level of measurement of the data.
(a) Family history of illness
(b) Happiness level ( scale of 0 to 10)
(c) Temperature
(d) Time since last visit

(a) What is the level of measurement for "family history of illness"?

( ) Ordinal
( ) Interval
( ) Nominal
( ) Ratio

(b) What is the level of measurement for "Happiness level (scale of 0 t0 10)?
( ) Ordinal
( ) Ratio
( ) interval
( ) Nominal

(c) What is the level of measurement for Temperature"?
( ) Ordinal
( ) ratio
( ) Interval
( ) Nominal

(d) What is the level of measurement for "Time since last visit"?
( ) Interval
( ) Ration
( ) Nominal
( ) Ordinal

8. Determine whether the statement is true or false. If is false, rewrite it as a true statement.
More types of calculation can be performed with data at the interval level than with data at nominal level.
( ) A. False. More types of calculations can be performed with data at interval level than with data at the nominal level
( ) B. True.
( ) C. False. The same types of calculations can be performed with data at the nominal level and with data at the interval level.

9. Decide which method of data collection you would use to collect data for the study
A study of the effect on the taste of a snack food made with a fat substitute.
A. Simulation
B. Experiment
C. Survey
D. Observational Study

10. Decide which method of data collection you would use to collect data for the study described below.
A study of how fast a certain poison kills a human child.
A. Observational study
B. Simulation
C. Experiment
D. Survey

11. A Radio station asks its listeners to call in their opinion regarding the use of pesticides in residential areas.
What type of sampling is used?
A. Systematic
B. Simple random
C. Convenience
D. Stratified
E. Cluster

12. To determine customer opinion of their service, Business Depot randomly selects 120 stores during a certain week and surveys all customers present in the store.
What type of sampling is used?
A. Stratified
B. Convenience
C. Simple random
D. Systematic
E. Cluster

13. Nissan wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 70 customers and asks them about their level of satisfaction with the company.
What type of sampling is used?
A. Cluster
B. Systematic
C. Simple random
D. Stratified
E. Convenience

14. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 20th soup can that comes of the assembly line starting with the tenth until she obtains a sample of 60 soup cans.
What type of sampling is used/
A. Cluster
B. Systematic
C. Simple random
D. Convenience
E. Stratified

15. To determine her blood pressure, Jean divides up her day into three parts, morning, afternoon, and evening. She then measures her blood pleasure at 3 randomly selected times during each part of the day.
What type of sampling is used?
A. Stratified
B. Convenience
C. Simple random
D. Systematic
E. Cluster

16. Determine whether you would take a census or use sampling to collect data for the study described below.
The most popular house color among the 20 employees of a company.
Would you take a census or use a sampling?
( ) Census
( ) Sampling

17. Determine whether the survey question is biased. If the question is biased, suggest a better wording.
Why is eating eggs bad for you?
Is the question biased?
( ) No
( ) Yes

If the question is biased, which question below is worded better?
A. Do you think that eating eggs is bad for you?
B. How do you think eating eggs affects your health?
C. The original question is not biased.
D. Why is eating eggs good for you/
E. Do you think that eating eggs is good for you?

18. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
A. True
B. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.
C. False. The method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals.

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## 40 MULTIPLE CHOICE QUESTIONS

MULTIPLE CHOICE QUESTIONS

In the following multiple choice questions, circle the correct answer.

1. A numerical value used as a summary measure for a sample, such as sample mean, is known as a

a. population parameter
b. sample parameter
c. sample statistic
d. population mean
e. None of the above answers is correct.

2. Since the population size is always larger than the sample size, then the sample statistic

a. can never be larger than the population parameter
b. can never be equal to the population parameter
c. can never be zero
d. can never be smaller than the population parameter
e. None of the above answers is correct.

3. Mu is an example of a

a. population parameter
b. sample statistic
c. population variance
d. mode
e. None of the above answers is correct.

4. The mean of a sample is
a. always equal to the mean of the population
b. always smaller than the mean of the population
c. computed by summing the data values and dividing the sum by (n - 1)
d. computed by summing all the data values and dividing the sum by the number of items
e. None of the above answers is correct.

5. The sum of the percent frequencies for all classes will always equal

a. one
b. the number of classes
c. the number of items in the study
d. 100
e. None of the above answers is correct.

6. In a five number summary, which of the following is not used for data summarization?

a. the smallest value
b. the largest value
c. the median
d. the 25th percentile
e. the mean

7. Since the mode is the most frequently occurring data value, it

a. can never be larger than the mean
b. is always larger than the median
c. is always larger than the mean
d. must have a value of at least two
e. None of the above answers is correct.

Exhibit 3-1
The following data show the number of hours worked by 200 statistics students.

Number of Hours Frequency

0 - 9 40
10 - 19 50
20 - 29 70
30 - 39 40

8. Refer to Exhibit 3-1. The class width for this distribution

a. is 9
b. is 10
c. is 11
d. varies from class to class
e. None of the above answers is correct.

9. Refer to Exhibit 3-1. The number of students working 19 hours or less

a. is 40
b. is 50
c. is 90
d. can not be determined without the original data
e. None of the above answers is correct.

10. Refer to Exhibit 3-1. The relative frequency of students working 9 hours or less

a. is .2
b. is .45
c. is 40
d. can not be determined from the information given
e. None of the above answers is correct.

11. Refer to Exhibit 3-1. The cumulative relative frequency for the class of 10 - 19

a. is 90
b. is .25
c. is .45
d. can not be determined from the information given
e. None of the above answers is correct.

12. The difference between the largest and the smallest data values is the

a. variance
b. interquartile range
c. range
d. coefficient of variation
e. None of the above answers is correct.

13. Which of the following is not a measure of central location?

a. mean
b. median
c. variance
d. mode
e. None of the above answers is correct.

14. If a data set has an even number of observations, the median

a. can not be determined
b. is the average value of the two middle items
c. must be equal to the mean
d. is the average value of the two middle items when all items are arranged in ascending order
e. None of the above answers is correct.
15. The sum of deviations of the individual data elements from their mean is

a. always greater than zero
b. always less than zero
c. sometimes greater than and sometimes less than zero, depending on the data elements
d. always equal to zero
e. None of the above answers is correct.

16. The value that has half of the observations above it and half the observations below it is called the

a. range
b. median
c. mean
d. mode
e. None of the above answers is correct.

17. The most frequently occurring value of a data set is called the

a. range
b. mode
c. mean
d. median
e. None of the above answers is correct.

18.. In a sample of 800 students in a university, 160, or 20%, are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of

a. a sample
b. a population
c. statistical inference
d. descriptive statistics
e. None of the above answers is correct.

19.. A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 21 years. This is an example of

a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
e. None of the above answers is correct.

20. A tabular summary of a set of data showing the fraction of the total number of items in several classes is a

a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
e. None of the above answers is correct.

21. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

a. 8
b. 10
c. 6,400
d. 4,096
e. None of the above answers is correct.

22. The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals

a. 0
b. 4096
c. 8
d. 6,561
e. None of the above answers is correct.

Exhibit 3-2
A researcher has collected the following sample data.

5 12 6 8 5
6 7 5 12 4

23. Refer to Exhibit 3-2. The median is

a. 5
b. 6
c. 7
d. 8
e. None of the above answers is correct.

24. Refer to Exhibit 3-2. The mode is

a. 5
b. 6
c. 7
d. 8
e. None of the above answers is correct.

25. Refer to Exhibit 3-2. The mean is

a. 5
b. 6
c. 7
d. 8
e. None of the above answers is correct.

Exhibit 3-3
A researcher has collected the following sample data. The mean of the sample is 5.
3 5 12 3 2

26. Refer to Exhibit 3-3. The variance is

a. 80
b. 4.062
c. 13.2
d. 16.5
e. None of the above answers is correct.

27. Refer to Exhibit 3-3. The standard deviation is

a. 8.944
b. 4.062
c. 13.2
d. 16.5
e. None of the above answers is correct.

28. Refer to Exhibit 3-3. The coefficient of variation is

a. 72.66%
b. 81.24%
c. 264%
d. 330%
e. None of the above answers is correct.

29. Refer to Exhibit 3-3. The range is

a. 1
b. 2
c. 10
d. 12
e. None of the above answers is correct.

30. Refer to Exhibit 3-3. The interquartile range is

a. 1
b. 2
c. 10
d. 12
e. None of the above answers is correct.

Exhibit 3-4
The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed
Miles per Hour Frequency
50 - 54 2
55 - 59 4
60 - 64 5
65 - 69 10
70 - 74 9
75 - 79 5
35

31. Refer to Exhibit 3-4. The mean is

a. 35
b. 670
c. 10
d. 67
e. None of the above answers is correct.

32. Refer to Exhibit 3-4. The variance is

a. 6.969
b. 7.071
c. 48.570
d. 50.000
e. None of the above answers is correct.

33. Refer to Exhibit 3-4. The standard deviation is

a. 6.969
b. 7.071
c. 48.570
d. 50.000
e. None of the above answers is correct.

34. Which of the following is not a measure of dispersion?

a. the range
b. the 50th percentile
c. the standard deviation
d. the interquartile range
e. the variance

35. If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?

a. the data set is a sample
b. the data set is a population
c. the data set could be either a sample or a population
d. the data set is from a census
e. None of the above answers is correct.

36. In computing descriptive statistics from grouped data,

a. data values are treated as if they occur at the midpoint of a class
b. the grouped data result is more accurate than the ungrouped result
c. the grouped data computations are used only when a population is being analyzed
d. All of the above answers are correct.
e. None of the above answers is correct.

37. The measure of dispersion that is influenced most by extreme values is

a. the variance
b. the standard deviation
c. the range
d. the interquartile range
e. None of the above answers is correct.

38. When should measures of location and dispersion be computed from grouped data rather than from individual data values?

a. as much as possible since computations are easier
b. only when individual data values are unavailable
c. whenever computer packages for descriptive statistics are unavailable
d. only when the data are from a population
e. None of the above answers is correct.

39. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

a. the range
b. the interquartile range
c. both a and b
d. the standard deviation
e. None of the above answers is correct.