Chapter 10: Hypothesis Testing Using a Single Sample
Concept Quiz
Name _________________________
The following questions are in a True / False format. The answers to these questions will
frequently depend on remembering facts, understanding of the concepts, and knowing the
statistical vocabulary. Before answering these questions, be sure to read them carefully!
T
F
1. The statement s 2  100 is a statistical hypothesis.
T
F
2. The choice of the alternative hypothesis depends on the objectives of the
study.
T
F
3. If the null hypothesis is not rejected, there is strong statistical evidence that
the null hypothesis is true.
T
F
4. A type II error is made by failing to reject a false null hypothesis.
T
F
5. The level of significance of a test is the probability of making a type I
error, given that the null hypothesis is true.
T
F
6. All other things being equal, choosing a smaller value of  will increase
the probability of making a type II error.
T
F
7. Small P-values indicate that the observed sample is inconsistent with the
null hypothesis.
T
F
8. It is customary to say that the result of a hypothesis test is statistically
significant when the P-value is smaller than  .
T
F
9. The power of a test is the probability of failing to reject the null
hypothesis.
T
F
10.
T
F
11. For tests of hypotheses about  ,  decreases as the sample size increases
if the level of significance stays the same.
 is called the observed significance level.
Chapter 10, Review Packet
Page 1 of 7
Chapter 10: Hypothesis Testing Using a Single Sample
Section 10.1-10.2
Name ___________________________
1. Explain in your own words what a hypothesis test is.
2. Explain in your own words the distinction between a null and alternative hypothesis.
Chapter 10, Review Packet
Page 2 of 7
3. Children as young as 2 years of age, upon seeing an object placed under a pillow in a
familiar setting at home, will understand to look for it after an interval of time and be
able to find it. Investigators believe this capability will be less pronounced in a
laboratory situation, where the child is away from the familiar setting of home. Let
p denote the proportion of 2-year-olds than have this understanding in the home
situation, and suppose that p = .35 . The investigators wish to determine whether the
proportion that remembers is less when the child is away from home.
a) What is the appropriate null hypothesis?
b) What is the appropriate alternative hypothesis?
c) In your own words, distinguish between a Type I and a Type II error in this context.
Chapter 10, Review Packet
Page 3 of 7
4. The Environmental Protection Agency (EPA) is charged with monitoring the
environment. One aspect of this is keeping track of "acid rain," a broad term
describing the fall of water through an acidic atmosphere. Acidity is measured on the
pH scale, where pure water has a pH of 7.0. Normal rain is slightly acidic because
carbon dioxide dissolves into it, and thus has a pH of about 5.5. (A lower pH
indicates greater acidity.) Suppose the EPA wishes to determine whether a particular
area is subject to acid rain. Let m denote the true average for pH in this area.
a) What is the appropriate null hypothesis?
b) What is the appropriate alternative hypothesis?
c) In your own words, distinguish between a Type I and a Type II error in this context.
Chapter 10, Review Packet
Page 4 of 7
Chapter 10: Hypothesis Testing Using a Single Sample
Section 10.3-10.4
Name ___________________________
1. Define, using your own words, a test statistic.
2. In your own words, what is a P-Value?
Chapter 10, Review Packet
Page 5 of 7
3. As children grow they develop what is known as "representational insight," a
connection between an object and a symbol for that object. A random sample of
youngsters 24-months old were shown a video of someone putting a toy under 1 of 4
randomly placed boxes in a room familiar to the child. They were then taken to the
room, and asked to "find the toy." The investigators reasoned that a child with
representational insight should pick the correct box on the first try. If the children
were to overturn the boxes randomly, they would find the toy on the first turn 25% of
the time. Thirty children out of 57 subjects found the toy by turning over the correct
box on the first try.
Does this sample provide sufficient evidence that the proportion of 24-month old
children who choose the correct box on the first try is greater than 0.25? Use a
significance level of a = .05 to test the appropriate hypothesis.
Chapter 10, Review Packet
Page 6 of 7
4. The department of natural resources defines a fish to be unsafe to eat if the
polychlorinated biphenol (PCB) concentration exceeds 5 parts per billion (ppb). A
random sample of 10 fish taken from a local lake resulted in the data listed below:
2.6, 6.6, 4.8, 5.4, 5.1, 4.5, 6.9, 4.9, 3.7, 3.8
Is there sufficient evidence to conclude that the mean PCB concentration for fish
from this lake exceeds 5 ppb?
Chapter 10, Review Packet
Page 7 of 7