QUESTION
 
1. (A) Classify the following as an example of nominal, ordinal, interval, or ratio
 
level of measurement, and state why it represents this level: distance between two
 
signposts
 
(B) Determine if this data is qualitative or quantitative: Brown eyes
 
(C) In your own line of work, give one example of a discrete and one example
 
of a continuous
 
random variable, and describe why each is continuous or discrete.
 
2. A researcher wants to determine if teenage drivers of red automobiles are more
 
likely to run a red light than automobiles of any other color. She stands at a
 
busy intersection and records the colors of automobiles which run red lights.
 
I. What is the population?
 
II. What is the sample?
 
III. Is the study observational or experimental? Justify your answer.
 
IV. What are the variables?
 
V. For each of those variables, what level of measurement (nominal, ordinal,
 
interval, or ratio) was used to obtain data from these variables?
 
3. Construct both an ungrouped and a grouped frequency distribution for the data
 
given below:
 
119 115 111 107 109 119 116 107 111 112
 
115 107 110 114 110 107 106 105 105 113
 
4. Given the following frequency distribution, find the mean, variance, and
 
standard deviation. Please show all of your work.
 
Class Frequency
 
56-58 22
 
59-61 14
 
62-64 24
 
65-67 19
 
68-70 19
 
5. The following data lists the average monthly snowfall for January in 15 cities
 
around the US:
 
37 33 35 27 9 45 22 8
 
42 48 37 39 9 15 12
 
Find the mean, variance, and standard deviation. Please show all of your work.
 
6. Rank the following data in increasing order and find the positions and values of
 
both the 39th percentile and 73rd
 
percentile. Please show all of your work.
 
5 5 0 0 9 6 8 9 2 6 3 8
 
7. For the table that follows, answer the following questions:
 
x y
 
1 -1/3
 
2 -2/3
 
3 -1
 
4
 
– Would the correlation between x and y in the table above be positive or
 
negative?
 
– Find the missing value of y in the table.
 
– How would the values of this table be interpreted in terms of linear
 
regression?
 
– If a “line of best fit” is placed among these points plotted on a coordinate
 
system, would the slope of this line be positive or negative?
 
8. Determine whether each of the distributions given below represents a probability
 
distribution. Justify your answer.
 
(A)
 
x 1 2 3 4
 
P(x) 1/12 5/12 1/3 1/6
 
(B)
 
x 3 6 8
 
P(x) 0.2 3/5 0.3
 
(C)
 
x 20 30 40 50
 
P(x) 0.1 0.1 0.5 0.3
 
9. A set of 50 data values has a mean of 20 and a variance of 36.
 
I. Find the standard score (z) for a data value = 18.
 
II. Find the probability of a data value < 18.
 
III. Find the probability of a data value > 18.
 
Show all work.
 
10. Answer the following:
 
(A) Find the binomial probability P(x = 4), where n = 14 and p = 0.60.
 
(B) Set up, without solving, the binomial probability P(x is at most 4) using
 
probability notation.
 
(C) How would you find the normal approximation to the binomial probability P(x =
 
4) in part A? Please show how you would calculate µ and σ in the formula for the
 
normal approximation to the binomial, and show the final formula you would use
 
without going through all the calculations.
 
11. Assume that the population of heights of female college students is
 
approximately normally distributed with mean µ of 64.43 inches and standard
 
deviation σ of 4.61 inches. A random sample of 89 heights is obtained. Show all
 
work.
 
(A) Find P(x bar > 65.25)
 
(B) Find the mean and standard error of the x bar distribution
 
(C) Find P(x bar > 65.25)
 
(D) Why is the formula required to solve (A) different than (C)?
 
12. Determine the critical region and critical values for z that would be used to
 
test the null hypothesis at the given level of significance, as described in each
 
of the following:
 
(A) and , α = 0.01
 
(B) and , α = 0.05
 
(C) and , α = 0.10
 
13. Describe what a type I and type II error would be for each of the following
 
null hypotheses:
 
1. : This fast-food menu is not low fat.
 
14. A researcher claims that the average age of people who buy theatre tickets
 
is 44. A sample of 30 is selected and their ages are recorded as shown below.
 
The standard deviation is 7. At α = 0.05 is there enough evidence to reject the
 
researcher’s claim? Show all work.
 
45 38 60 45 63 37 45 43 52 48
 
67 38 45 44 41 45 50 45 55 39
 
45 46 57 41 39 41 66 39 39 55
 
15. Write a correct null and alternative hypothesis that tests the claim that the
 
mean distance a student commutes to campus is no less than 6.4 miles?