1.A) Classify the following as an example of nominal, ordinal, interval, or
ratio level of measurement, and state why it represents this level: major
field of study of 100 college students
(B) Determine if this data is qualitative or quantitative: Red hair
(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
2.A large group of teenagers is divided into two smaller groups of 125 each,
and each group watches a different movie. One group watches a love story
while the other group watches a movie containing several scenes with
violence. The teenagers are then asked questions to uncover unconscious
associations and determine their level of aggression.
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:
42 46 52 50 54 51 51 49 54 42
55 49 53 50 55 41 53 52 47 45
4.Given the following frequency distribution, find the mean, variance, and
standard deviation. Please show all of your work.
5.The following data lists the average monthly snowfall for January in 15
cities around the US:
43 16 38 28 7 31 18 37
35 5 43 23 24 29 22
Find the mean, variance, and standard deviation. Please show all of your
6.Rank the following data in increasing order and find the positions and
values of both the 36th percentile and 58th
percentile. Please show all of your work.
5 5 1 3 8 7 7 7 0 0 9 8
7. For the table that follows, answer the following questions:
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
- 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.
x 1 2 3 4
P(x) 0.25 5/12 1/3 1/6
x 3 6 8
P(x) 0.1 3/5 0.3
x 20 30 40 50
P(x) 0.2 - 0.7 0.3
9.A set of 50 data values has a mean of 22 and a variance of 16.
I. Find the standard score (z) for a data value = 14.
II. Find the probability of a data value < 14.
III. Find the probability of a data value > 14.
Show all work.
10.Answer the following:
(A) Find the binomial probability P(x = 6), where n = 12 and p = 0.30.
(B) Set up, without solving, the binomial probability P(x is at most 6) using
(C) How would you find the normal approximation to the binomial probability
P(x = 6) 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 male college students is
approximately normally distributed with mean of 73.16 inches and standard
deviation of 6.39 inches. A random sample of 70 heights is obtained. Show
(A) Find p(x>74.50)
(B) Find the mean and standard error of the xbar distribution
(C) Find p(xbar> 74.50)
(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 , = 0.05
(B) and , = 0.10
(C) and, = 0.01
13.Describe what a type I and type II error would be for each of the following
: This is not the least expensive dishwasher.
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
= 0.05 is there enough evidence to reject the researcher’s claim? Show all
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
a correct null and alternative hypothesis for testing the claim that
the mean life of a battery for a cell phone is at least 55 hours.