Download AP StatisticsHypothesis Testing Review

AP Statistics
Hypothesis Testing Review
Name_____________________ Hr___
1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A)
a statement of "no effect" or "no difference."
B)
the probability of observing the data you actually obtained.
C)
a statement that the data are all 0.
D)
0.05.
2. Suppose we are testing the null hypothesis H 0 :   50 and the alternative H a :   50 ,
for a normal population with  = 6. A random sample of nine observations are drawn
from the population and x = 53. The P-value is closest to
A)
0.0668.
B)
0.1336.
C)
0.0332.
D)
0.3085.
3. The mean area  of the several thousand apartments in a new development is advertised
to be 1250 square feet. A tenant group thinks that the apartments are smaller than
advertised. They hire an engineer to measure a sample of apartments to test their
suspicion. The appropriate null and alternative hypotheses, H 0 and H a , for  are
B)
H 0 :   1250 vs. H a :   1250 .
H 0 :   1250 and H a :   1250 .
C)
D)
H 0 :   1250 and H a :   1250 .
cannot be specified without knowing the size of the sample used by the engineer.
A)
4. The P-value of a test of a null hypothesis is
A)
the probability, assuming the null hypothesis is true, that the test statistic will take
a value at least as extreme as that actually observed.
B)
the probability, assuming the null hypothesis is false, that the test statistic will
take a value at least as extreme as that actually observed.
C)
the probability that the null hypothesis is true.
D)
the probability that the null hypothesis is false.
5. Newly purchased automobile tires of a certain type are supposed to be filled to a pressure
of 30 psi. Let μ denote the true average pressure. (We are assuming that σ is known.)
a) Find the P-value associated with 𝑧 = −.58 for testing 𝐻0 : 𝜇 = 30 versus 𝐻𝑎 : 𝜇 > 30.
b) Find the P-value associated with 𝑧 = 1.44 for testing 𝐻0 : 𝜇 = 30 versus 𝐻𝑎 : 𝜇 ≠ 30.
AP Statistics
Hypothesis Testing Review
6. Mr. Wichman and Mrs. Sapp both believe that the average mathematically-inclined
student at MHS can score significantly higher than 90 on the American Mathematics
Examination (AMC). (It is known that the population standard deviation is 6.54.) They
take a simple random of 40 MHS students’ AMC scores and find that the overall average
is 91.3.
a. State null and alternative hypotheses suitable for testing Mr. Wichman and Mrs.
Sapp’s claim. Be sure to define your variable(s).
b. State your assumptions.
c. Compute the P-value associated with x  91.3 .
d. At a level of significance   .05 , what is the outcome? That is, shall you reject
at this level?
e. (3 points) A non-mathematically inclined person could conceivably argue that
91.3 is not much greater than 90 and hence Mr.Wichman and Mrs. Sapp’s claim
cannot possibly be true. How would you respond to this?
7. In a discussion of the educational level of the American workforce, someone says, “The
average young person can’t even balance a checkbook.” The National Assessment of
Educational Progress (NAEP) says that a score of 275 or higher on its quantitative test
reflects the skill needed to balance a checkbook. The NAEP random sample of 840 young
men had a mean score of x  272 , a bit below the checkbook-balancing level. Suppose
NAEP knows from experience that the standard deviation of scores in the population of
all young men is   60 . Is this sample result good evidence that the mean for all young
men is less than 275?
AP Statistics
Hypothesis Testing Review
8. Which of the following statements is not true?
A. A researcher who rejects a true null hypothesis has committed a Type I error.
B. A researcher who rejects the null hypothesis has computed a test statistic that is large in
absolute value.
C. A researcher who rejects the null hypothesis has computed a P-value that is large in
value.
D. When the null hypothesis is true, the probability of making a Type I error is equal to the
significance level.
E. Increasing the sample size has no effect on the probability of making a Type I error.
9. The power of a test is
A. the probability that you will make a correct decision, regardless of what is true
B. the probability of rejecting the alternate hypothesis if the hypothesized value is true
C. the probability of failing to reject the null hypothesis if an alternative value is true
D. the probability of correctly rejecting the null hypothesis if an alternative value is true
E. the probability of failing to reject the alternate hypothesis if the hypothesized value is true
10. A certain population follows a normal distribution with mean  and standard deviation
= 22.1. You collect data on four members of the population and test the hypotheses
H 0 :   100 , H 0 :   100
You obtain a P-value of 0.052. Which of the following is true?

A. At the 5% significance level, you have proved that H 0 is true.
B. You have failed to obtain any evidence for H a
C. There is some evidence against H 0 , and a study using a larger sample size may be
worthwhile.
D. This should be viewed as a pilot study, and the data suggests that further investigation of
the hypotheses will not be fruitful at the 5% significance level.
11. Fill in the following chart. Be sure to include Type I and II errors, α, β, and Power of
the test.
𝐻0 true
FAIL TO REJECT
REJECT
𝐻0 false
AP Statistics
Hypothesis Testing Review
12. 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 acid
from the 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 subjected to acid rain. Let μ 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.
Is one more serious than the other? Explain.
13. An agricultural field trial compares the yield of two varieties of tomatoes for commercial use.
The researchers divide in half each of 10 small plots of land in different locations and plant
each tomato variety on one half of each plot. After harvest, they compare the yields in
pounds per plant at each location. The 10 differences (Variety A – Variety B) give x  .34 .
The researchers assume a population standard deviation of .83 based on previous data. Is
there convincing evidence that variety A has the higher mean yield?
14. I draw an SRS of size 15 from a population that has a normal distribution with mean 
and standard deviation  . The one-sample t statistic has how many degrees of freedom?
15. What is the value of t*, the critical value of the t distribution with n=9, which satisfies the
condition that the probability is 0.10 of being larger than t*?
A)
1.397.
B)
1.282.
C)
2.896.
D)
1.860.
AP Statistics
Hypothesis Testing Review
16. Scores on the SAT Mathematics test (SAT-M) are believed to be normally distributed
with mean  . The scores of a random sample of three students who recently took the
exam are 550, 620, and 480. Find and interpret a 95% confidence interval for  based
on these data.
17. An SRS of 100 postal employees found that the average time these employees had
worked for the postal service was x = 7 years with standard deviation s = 2 years.
Assume the distribution of the time the population of employees have worked for the
postal service is approximately normal with mean  .
a) Are these data evidence that  has changed from the value of 7.5 years of 20 years
ago?
b) Find and interpret a 95% confidence interval for the mean time 𝜇 the postal lab
employees have spent with the lab.
18. When the hatching of young geese is very near, the father guards the nest to defend it
from predators that may be attracted by the hatchlings’ noisy entrance into the world. A
biologist believes that the mean distance father geese roam from the nest is less than
5.8m. The following data are the typical distances from the nest for 24 soon-to-be father
geese. Test the biologist’s hypothesis.
2.0
4.4
6.3
5.6
4.5
4.7
5.0
5.4
5.6
5.9
5.5
4.9
5.7
5.3
5.6
5.4
5.7
5.4
5.3
5.3
4.9
5.6
5.2
4.5