Online Midterm Exam
Part A: True or False (1-10)
In a frequency distribution, the class mark is the number of observations that fall within that class. The random sample is the most important, because statistical theory applies to it alone
3. The sum of the class frequencies is equal to the number of observations made There would be no need for statistical theory if census , rather than a sample was always used to obtain information about populations. Planning is the most important step in statistical study
A relative frequency distribution describes the proportion of data values that fall within each category.
The arithmetic mean is the sum of the data values divided by the number of observations.
For the data, 35, 22, 18, and 25, the value of the median is 20.
______ 9. The median always exists in a set of numerical data.
______ 10.The P(x) is always 0 ≤ P(x) ≤ 1.
Part B: Answer the following questions (11-19)
Name 6 reasons why we use samples instead of an entire population.
Name 3 types of statistical samples
Name measures of spread or variability.
Name 4 types of random samples.
Show that you understand the difference between a sample and a population
Explain the following terms (a-e):
Random variable
Random sample
Percentile
Quartile
Sturges' rule
What is regression analysis?
Name 4 parts of the regression.
When do we use the regression?
Part C: Multiple Choice (20-26)
Please select the best answer for 6-8:
_____ 20. The simplest measure of dispersion is the
a.) Standard deviation. b.) Variance.
c.) Quartile deviation d.) Range
_____ 21. The largest value in a set of data is 240, and the lowest value is 100. If the resulting frequency distribution is to have seven classes of equal width, what will be the class width?
a.) 12 b.) 7 c.) 5 d.) 20
_____ 22. For the values 10, 20, 30, 40, and 50, the average absolute deviation from the mean is
a.) 10 b.) 15 c.) 12 d.) 14
Use the information below to answer question 23-26:
Eye Color
Hair Color Blond Brown Blue Green Hazel
Blond 30 18 7 2 57
Brown 74 28 10 7 119
Red/Auburn 17 15 5 3 40
Black 43 11 6 1 61
164 72 28 13 277
From the above cross Classification showing the frequencies of hair and eye color of a group of students at North Texas, compute the following:
_____ 23.Probability of black hair.
0.61 b.) 61 c.) 0.43 d.) 0.22 e.) 0.78
_____ 24.Probability that a student will have blue eyes given he/she is blond.
1-0.18 b.) 0.18 c.) 18/72 d.) 18/57 e.) 18/277
_____ 25.Probability that a student will have brown hair and brown eyes.
0.74 b.) 74/164 c.) 119/277*164/277 d.) 74/119 e.) 74/277
_____ 26.Probability that a student will have either red hair or green eyes.
63/277 b.) 5/277 c.) 5/28 d.) 68/277 e.) 5/40
Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (27-40)
The following random sample of annual salaries was recorded. Units are in thousands of dollars. Please use the following data to answer the questions.
50 52 48 46 32 51 47 20 53 49
Mean
Median
Variance
Standard deviation
Percentile 75th
Please compute and fill the following table (**Using D-Method). Then answer the following questions
Class Frequency Mid-point (X) Cf d df d2 d2f
60-64 1 -3
65-69 12 -2
70-74 3 -1
75-79 10 0
80-84 11 1
85-89 3 2
90-94 4 3
Total
Mean
Q2
Variance
Standard deviation
Percentile 75th
Advertising expenditures constitute one of the important components of the cost of goods sold. From the given data, the advertising expenditures (in millions of dollars) of 50 companies. Please compute and fill the following table (**Using D-Method). Then answer the following questions
Advertising Expenditure Number of company Mid-point (X) Cf d df d2 d2f
25-35 5 -2
35-45 18 -1
45-55 11 0
55-65 6 1
65-75 10 2
Total 50
Mean
P50
Variance
Standard deviation
Percentile 80th
Work on problem number 2 on page 3-55
Work on problem number 3 on page 3-55
Work on problem number 1 (a-e) on page 4-10
**Given that X = Media Expenditure, Y = Case Sales
The following table has been prepared from a survey of 100 companies in three industries:
Computer Type
Industry IBM Apple IBM compatible Total
Banking 25 5 5 35
Electronics 10 20 10 40
Accounting 25 0 0 25
Total 60 25 15 100
To determine the primary type of microcomputer used by employees in the companies, suppose one of these 100 surveyed companies is chosen at random, and answer the following questions:
P(IBM)
P(IBM or Electronics)
P(Apple and Banking)
P(IBM and Apple)
Work on problem number 3 (a-f) on page 6-15
Work on problem number 12 (a-e) on page 6-19
Work on problem number 5 (a-f) on page 6-20
Work on problem number 4 on page 6-31
Given the following probabilities, find Z0 and please draw the shading the area:
Show your work Please draw graph
a. P(Z≤Z_0 )=0.0055
b. P(-2.67≤?Z≤Z?_0 )=0.9718
c. P(Z>Z_0 )=0.0384
d. P(Z_0≤Z≤2.98)=0.1117
e. P(Z>Z_0 )=0.85
f. P(Z_0≤?Z≤Z?_0 )=0.95
Using the standard normal distribution tables, determine the following probabilities and please draw the shading the area
Show your work Please draw graph
a. P(0.00b. P(2.00c. P(-1.25d. P(-2.5e. P(Z>0.80)
f. P(Z<0.90)
Find the percentage of Z-score in a normal distribution with μ=75 and σ^2=100 that are:
Between 60 and 80
Between 40 and 65
Greater than 83
Less than 67