Stat 200 Midterm Exam                                                                 Name ___________________________________

 

Multiple Choice (1 pt each)

 

1. Quantitative data
   1. are always nonnumeric
   2. may be either numeric or nonnumeric
   3. are always numeric
   4. None of these alternatives is correct.

 

1. The 50th percentile is the

1. mode
2. median
3. mean
4. third quartile
6. In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a
   1. qualitative variable
   2. quantitative variable
   3. qualitative or quantitative variable, depending on how the respondents answered the question
   4. None of these alternatives is correct.

 

4. Qualitative data
   1. indicate either how much or how many
   2. can not be numeric
   3. are labels used to identify attributes of elements
   4. must be nonnumeric

 

5. Statistical inference
   1. refers to the process of drawing inferences about the sample based on the characteristics of the population
   2. is the same as descriptive statistics
   3. is the process of drawing inferences about the population based on the information taken from the sample
   4. is the same as a census

 

6. For ease of data entry into a university database, 1 denotes that the student is an undergraduate and 2 indicates that the student is a graduate student. In this case data are
   1. qualitative
   2. quantitative
   3. either qualitative or quantitative
   4. neither qualitative nor quantitative

 

7. A portion of the population selected to represent the population is called
   1. statistical inference
   2. descriptive statistics
   3. a census
   4. a sample

 

 

8. Qualitative data
   1. must be numeric
   2. must be nonnumeric
   3. cannot be numeric
   4. may be either numeric or nonnumeric

 

9. The summaries of data, which may be tabular, graphical, or numerical, are referred to as
   1. inferential statistics
   2. descriptive statistics
   3. statistical inference
   4. report generation

 

10. In a sample of 400 students in a university, 80, or 20%, are Business majors. Based on the above information, the school’s newspaper reported that “20% of all the students at the university are Business majors.”  This report is an example of
    1. a sample
    2. a population
    3. statistical inference
    4. descriptive statistics

 

1. The sum of the relative frequencies for all classes will always equal

1. the sample size
2. the number of classes
3. one
4. any value larger than one

 

12. In a sample of 800 students in a university, 240, or 30%, are Business majors. The 30% is an example of
    1. a sample
    2. a population
    3. statistical inference
    4. descriptive statistics

 

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

1. 1. one
   2. the number of classes
   3. the number of items in the study
   4. 100

 

1. The variance of a sample of 169 observations equals 576.  The standard deviation of the sample equals

1. 13
2. 24
3. 576
4. 28,461

 

1. The sum of deviations of the individual data elements from their mean is

1. always greater than zero
2. always less than zero
3. sometimes greater than and sometimes less than zero, depending on the data elements
4. always equal to zero

 

 

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

1. variance
2. interquartile range
3. range
4. coefficient of variation

 

1. During a cold winter, the temperature stayed below zero for ten days.  The range was -20 to -5. The variance of the temperatures:

1. is negative since all the numbers are negative
2. must be at least zero
3. cannot be computed since all the numbers are negative
4. can be either negative or positive

 

1. If the mean of a distribution is negative,

1. the standard deviation must also be negative.
2. the variance must also be negative.
3. a mistake has been made in the computations, because the mean of a normal distribution can not be negative.
4. none of these alternatives is correct.

 

1. If two groups of numbers have the same mean, then

1. their standard deviations must also be equal
2. their medians must also be equal
3. their modes must also be equal
4. none of these alternatives is correct

 

 

 

Yes/No Questions

 

1. Can a sample have no mean?

 

1. Can a sample have the mean equal to the standard deviation?

 

1. Can the mean of a set of data be negative?

 

1. If a constant amount is added to all elements in a data set, does the mean change?

 

1. Can a sample have a variance of zero?

 

1. Can a sample have no variance?

 

1. Can the standard deviation of a set of data be negative?

 

1. If a constant amount is added to all elements in a data set, does the standard deviation change?

 

1. Can a sample have the mean, median and mode all equal each other?

 

1. If a constant amount is added to all elements in a data set, does the median change?

 

1. Can the median of a set of data be negative?

1. After the graduation ceremonies at a university, six graduates were asked whether they were in favor of (identified by 1) or against (identified by 0) abortion. Some information about these graduates is shown below.

 

Graduate             Sex         Age                        Abortion Issue         Rank

Nancy                     F                52                           1                                      1

Michael                  M              24                           1                                      2

Tammy                   F                33                           0                                      4

Edward                   M              38                           0                                    20

Jennifer                 F                25                           1                                      3

Tim                           M              19                           0                                      8

 

Name the variables and group them as qualitative and quantitative.

 

                Qualitative:

 

                Quantitative:

 

 

 

 

 

2. Forbes magazine published data on the best small firms in 1993. These were firms with annual sales of more

than five and less than $350 million. Firms were ranked by five-year average return on investment. The data

extracted are the age and annual salary of the chief executive officer for the first 60 ranked firms. Here are the

ages of those 60 CEOs.

32     33     36     37     38     40     41     43     43     44

44     45     45     45     45     46     46     47     47     47

48     48     48     48     49     50     50     50     50     50

50     51     51     52     53     53     53     55     55     55

56     56     56     56     57     57     58     58     59     60

61     61     61     62     62     63     64     69     70     74

 

1. Construct the frequency distributions for these data using the following classes.

 

Class	Frequency	Relative Frequency	Percent Frequency	Cumulative Percent Frequency
30£x<35
35£x<40
40£x<45
45£x<50
50£x<55
55£x<60
60£x<65
65£x<70
70£x<75
Sum

 

 

 

1. Approximately what percentage of CEOs are 50 years old or greater? Show work.

 

1. Create the absolute frequency Histogram

 

1. Create the percent frequency ogive

 

1. State whether the mean is greater than, less than, or approximately equal to the median. Explain why.

 

1. Which is a better representative of the typical CEO age, the mean or the median? Explain why.

 

 

 

 

3. Sixty-five percent of the applications received for a particular position are rejected.

 

1. What is the probability that among the next 10 applications, 3 will be rejected?

Show work or show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

1. What is the probability that among the next 10 applications, more than half will be rejected?

Show work or show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

1. How many of the next 100 applications would you expect to be rejected?

Show work or show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

               

 

 

 

 

4. I have 7 leftover earrings in my jewelry box. How many “pairs” of mismatched earrings can be worn from these earrings?

Show work or show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

 

 

 

 

5. The following table presents the probability distribution for district sales of cars at for a local distributor.

 

Sales (100’s)            Probability P(x)

0                                   0.20

1                                   0.15

2                                   0.15

3                                   0.30

4                                   0.20

 

How many cars should the manager expect to sell on any given day?

State your answer as a complete sentence.

 

 

 

 

 

6. Scores on a recent national statistics exam were normally distributed with a mean of 70 and a standard deviation of 6. (Scores are given to the whole point.) If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?

Show the drawing of the problem.

Show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

 

 

7. The weight of items produced by a machine is normally distributed with a mean of 105 ounces and a standard deviation of 20 ounces.

 

1. What is the probability that a randomly selected item will weigh less than 85 ounces?

Show the drawing of the problem.

Show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

1. If 250 items weighed less than 85 ounces, how many items were produced by the machine?

State your answer as a complete sentence.

 

 

 

 

 

8. The mean yearly rainfall in Sydney, Australia, is about 135 mm and the standard deviation is about 65 mm (“Annual maximums of,” 2013). Assume rainfall is normally distributed.

 

1. State the random variable

 

1. Find the probability that the yearly rainfall is less than 100 mm.

Show the drawing of the problem.

Show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

1. If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or why not?

 

1. Find the probability that the yearly rainfall is between 140 and 250 mm.

Show the drawing of the problem.

Show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.

 

1. What rainfall amount are 90% of all yearly rainfalls more than? Show the drawing of the problem.

Show the drawing of the problem.

Show a screenshot of the software output and reference the software used (provide the website).

State your answer as a complete sentence.