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# Briefly describe the four levels of measurement, providing an example of each.

1. Briefly describe the four levels of measurement, providing an example of each.

2. Identify and justify which type of sampling (random, stratified, systematic, cluster, convenience) is used in the following examples.

a.) A market researcher polls 50 people at a local shopping mall.

b.) To avoid working late, a control analyst simply inspects the first 100 items produced in a day.

c.) A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers.

d.) A tax auditor selects every 1000th income tax return that is received.

e.) A market researcher selects 500 people from each of 10 cities.

3. The regional manager of a large company has asked company headquarters for an increase in his staff from 8 to 9 employees. For budgetary reasons, the company administration is reluctant to approve the increase. In order to resolve the debate, the manager and company administration agree to examine data regarding the staff size of other managers with similar scopes of responsibility (number of team members, sales area, etc.) to the regional manager. These data are presented below. Should the manager be given an increase in staff? Why or why not? Please show your work.

Size of manager’s staff Number of managers
5 people 21
6 people 39
7 people 31
8 people 98
9 people 12
10 people 11

4. Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

5. Marketing researchers are interested in exploring whether a relationship exists between age and amount of alcohol consumed. The researchers collect the following data:

Case Age Ounces of alcohol consumed per week
1 18 0
2 63 24
3 57 0
4 24 18
5 21 30
6 58 26
7 47 24
8 43 18
9 33 20
10 36 20
11 45 18
12 40 28
13 39
0
14 61 20
15 79 0
16 43 12
17 28 6
18 31 10
19 26 18
20 52 9
21 57 18
22 59 28
23 64 36
24 43 30
25 59 18
26 48 28
27 37 26
28 51 24
29 20 12
30 19 0

a.) Calculate the mean and standard deviation for age and ounces of alcohol, by hand. Show your work and explain what these measures mean.

b) Create an SPSS data file for the data provided above. Calculate the following for ounces of alcohol and age. Copy the Variable View, Data View, and Output Panel screens to Word and attach them to your exam.

Frequency table
Quartiles
Mean, median, and mode
Range, variance, and standard deviation
Histogram (1 for ‘ounces of alcohol’ and 1 for ‘age’)
Bar chart (‘ounces of alcohol’ by ‘age’)

c.) In a paragraph or two, describe all of the output you obtained in parts A and B. Be sure to describe the level of measure and the type of variable for each (independent/dependent) variable (‘ounces of alcohol’ and ‘age’). Also describe whether you think the data suggests that a relationship exists between ‘ounces of alcohol’ and ‘age’.

6. Management development participants have to take a standardized test to test their knowledge of company rules and regulations.

a.) The training coordinator is interested in examining how women are performing on the test. She takes a small sample of test scores (below). What is the best way she can summarize these scores using measures of central tendency?

70 68 66 73 77 95 69 64 95 71

b.) Suppose that among all participants, the mean test score is 70.07 and the standard deviation is 10.27. Use z-scores to interpret a raw score of 80. What is the corresponding z-score? How would you interpret this result? Show your work.

c.) The CEO wants to select only those persons who scored better than 95 percent of all participants for a special assignment. Assume a mean of 70.07 and a standard deviation of 10.27. Use z-scores to determine the minimum raw score required to be selected for this assignment.

7. The table below describes the smoking habits of a group of asthma sufferers. If one of the 1,156 people is randomly selected, find the probability that the person is a man or a heavy smoker. (5 points)

Nonsmoker Occasional smoker Regular
smoker Heavy smoker Total
Men 431 50 71 49 601
Women 382 48 86 39 555
Total 813 98 157 88 1156

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