Question

practice and application exercises

1. “the man poll” of 1014 randomly - selected american men ages 18 and older was taken by newsweek june 2 - 4, 2003. the data shown below are from the poll.

in general, how would you describe your health?

age	18 - 34	35 - 55	≥56
very good	37	39	32
good	28	28	28
fair	10	10	16
poor	2	4	8
dont know	0	0	1

a. describe the population and the sample of this poll.
b. for each man, what variable is measured? are the data quantitative (numerical) or qualitative (nonnumerical categories)?

1. the american association of nurse anesthetists journal (feb 2000) published the results of a study on the use of herbal medicines before surgery. of 500 surgical patients who were randomly selected for the study, 51% used herbal or alternative medicines prior to surgery.

a. describe the population and the sample of this study.
b. is the sample representative of the population? explain your answer.
c. for each patient, what variable is measured? are the data quantitative (numerical) or qualitative (non - numerical categories)?

1. the government of a large city needs to determine whether the citys residents will support the construction of a new jail. the government will conduct a survey of a sample of the citys residents. which one of the following procedures would be most appropriate for obtaining a sample of the citys residents?

a. survey a random sample of the employees and inmates at the old jail.
b. survey every fifth person who walks into city hall on a given day.
c. survey a random sample of persons within each geographic region of the city.
d. survey the first 200 people listed in the citys telephone directory.

1. the city council of a large city needs to know whether its residents will support the building of three new schools. the council decides to conduct a survey of a sample of the citys residents. which procedure would be most appropriate for obtaining a sample of the citys residents?

a. survey a random sample of teachers who live in the city.
b. survey 100 individuals who are randomly selected from a list of all people living in the state in which the city in question is located.
c. survey a random sample of persons within each neighborhood of the city.
d. survey every tenth person who enters city hall on a randomly selected day.
a questionnaire was given to students in an introductory statistics class during the first week of the course. one question asked, “how stressed have you been in the last 2 weeks, on a scale of 0 to 10, with 0 being not at all stressed and 10 being as stressed as possible?” the students’ responses are shown in the frequency distribution. use this frequency distribution to solve exercises 5 - 8.

stress rating	frequency
1	1
2	3
3	12
4	16
5	18
6	13
7	31
8	26
9	15
10	14

1. which stress rating describes the greatest number of students? how many students responded with this rating?
2. which stress rating describes the least number of students? how many students responded with this rating?
3. how many students were involved in this study?
4. how many students had a stress rating of 8 or more?
5. a random sample of 30 college students is selected. each student is asked how much time he or she spent on home - work during the previous week. the following times (in hours) are obtained:

16, 24, 18, 21, 18, 16, 18, 17, 15, 21, 19, 17, 17, 16, 19, 18, 15, 20, 17, 15, 17, 24, 19, 16, 20, 16, 19, 18, 17.
construct a frequency distribution for the data.

1. a random sample of 30 male college students is selected. each student is asked his height (to the nearest inch). the heights are as follows:

72, 70, 68, 72, 71, 71, 69, 73, 71, 73, 75, 66, 67, 75, 74, 75, 71, 72, 67, 72, 68, 67, 71, 73, 71, 72, 70, 75, 70.
construct a frequency distribution for the data.

Explanation:

Step1: Identify the problem - part a of question 1

The population is all American men ages 18 and older. The sample is the 1014 randomly - selected American men.

Step2: Identify the problem - part b of question 1

The variable is the self - described health status. It is qualitative (non - numerical) since it is in categories like Excellent, Very good, etc.

Step3: Identify the problem - part a of question 2

The population is all surgical patients in the United States. The sample is the 500 surgical patients who were randomly selected.

Step4: Identify the problem - part b of question 2

The sample may not be representative as it only includes patients from one study and may not reflect all surgical patients in the US.

Step5: Identify the problem - part c of question 2

The variable is the use of herbal alternative medicines. It is qualitative as it is a yes/no or categorical response.

Step6: Identify the problem - question 5

The stress rating with the greatest number of students is 7. The number of students with this rating is 31.

Step7: Identify the problem - question 6

The stress rating with the least number of students is 0. The number of students with this rating is 2.

Step8: Identify the problem - question 7

The total number of students involved in the study is the sum of all frequencies: \(2 + 1+3 + 12+16+18+13+31+26+15+14=151\).

Step9: Identify the problem - question 8

The number of students with a rating of 8 or more is \(26 + 15+14 = 55\).

Step10: Identify the problem - question 9

Hours Spent on Home - work	Frequency
16	10
17	7
18	8
19	6
20	3
21	1

Step11: Identify the problem - question 10

Height (inches)	Frequency
67	4
68	3
69	2
70	4
71	6
72	5
73	5
74	2
75	2

Answer:

1.

• a. Population: All American men ages 18 and older. Sample: 1014 randomly - selected American men.
• b. Variable: Self - described health status. Qualitative.

2.

• a. Population: All surgical patients in the US. Sample: 500 randomly - selected surgical patients.
• b. Not necessarily representative as it may not reflect all US surgical patients.
• c. Variable: Use of herbal alternative medicines. Qualitative.

1. Stress rating 7, 31 students.
2. Stress rating 0, 2 students.
3. 151 students.
4. 55 students.
5. See frequency distribution table above.
6. See frequency distribution table above.