A
1) Which of the following statements are true?
I.
If a population parameter is known, there is no reason to run a hypothesis test on that
population parameter.
II.
The P-value can be negative or positive depending upon whether the sample statistic is less
than or greater than the claimed value of the population parameter in the null hypothesis.
III. The P-value is based on a specific test statistic so it must be chosen before an experiment is
conducted.
a)
B
E
I only
b) II only c) III only
d) I and II
e) None are true
2) You conduct a hypothesis test and find a p-value of .025. Which of the following is true?
a) You can reject H0 at = .01.
b) You can reject H0 at  = .05.
c) You can accept H0 at  = .05.
d) You can say the probability that H0 is true is .025.
e) None of these are true.
3) Which of the following statements are true?
I.
II.
III.
It is helpful to examine your data before deciding whether to use a one-sided or a two-sided
hypothesis test.
If the P-value is .05, the probability that the null hypothesis is correct is .05.
The larger the P-value, the more evidence there is against the null hypothesis.
a) I only
b) II only
c) III only
d) I and III
e) None of the above gives the complete set of true responses.
E
4) Which of the following are true statements?
I.
The alternative hypothesis is stated in terms of a sample statistic.
II.
A large P-value is evidence for the alternative hypothesis.
III.
If a sample is large enough, the necessity for it to be a simple random sample is diminished.
a) I only
b) II only
c) III only
d) I and III
e) None of the above gives the complete set of true responses.
D
5) A farmer sampled sheep from a large herd to obtain a 90% confidence interval for the proportion of
sheep that had a hoof problem. The interval was (.07, .11). If the farmer had used a 95% confidence
interval instead, the confidence interval would have been
a) wider and would have a smaller margin of error than the 90% confidence interval.
b) narrower and would have a larger margin of error than the 90% confidence interval.
c) narrower and would have a smaller margin of error than the 90% confidence interval.
d)
wider and would have a larger margin of error than the 90% confidence interval.
e)
wider but the margin of error would be the same size as the 90% confidence interval.
With a higher confidence level, you need to be shooting at a bigger bucket
D
6) About 78% of the U.S. population claims that they visit the dentist at least once a year. A random
sample of 200 people is selected for a health study and the sample proportion of those who visited the
dentist at least once during the year is computed. Which one of the following gives, respectively, the
mean and standard deviation of the sampling distribution of the sample proportion who claim they visit
the dentist at least once a year?
a) 156, 12.49
b) 156, 5.86
c) 0.78, 0.012
d) 0.78, 0.029
.78∗ .22
µ = p = .78
C
200
= 0.029
7) The manager of a local book store performs a survey to estimate the proportion of books sold by the
store that are murder mysteries. A 95% confidence interval from this data is (.283, .419). What is the
proportion of books that are murder mysteries in this sample?
a) 0.419
b) 0.702
c) 0.351
d) 0.136
e)
0.068
p
B
σ=√
.283  .419
2
 .351
8) The U.S. Department of Transportation reported that 77% of all fatally injured automobile drivers were
intoxicated. A random sample of 27 records of automobile driver fatalities in Kit Carson County,
Colorado, showed that 15 involved an intoxicated driver. Which of the following procedures is the
appropriate for calculating the test statistic for these data?
.556  .77
.556  .77
.77  .556
.77  .56
a) z 
b) z 
c) z 
d) z 
e)
.556(.444 )
.77 (.23)
.556(.444 )
.556(.444 )
27
27
27
27
.77  .556
z 
.77 (.23)
27
p
15
 .556
27
Z
p p
p 1  p 
n

.556  .77
.77 .23 
27
In a recent survey of 1200 randomly selected high school students in the U.S., 36% said that newspapers
should get government approval before printing a news story. The sample data was used to construct a 95%
confidence interval of (0.332, 0.387) for the proportion of all students who would say that newspapers
should get government approval before printing a news story.
A
9) Based upon this confidence interval, what decision would you make for the hypothesis test of H 0: p = .3
versus Ha: p ≠ .3?
a)
We would reject the null hypothesis.
b)
c)
d)
We would accept the null hypothesis.
We would fail to reject the null hypothesis.
No decision can be made based upon this interval.
.3 is not in the confidence interval
10) In a random sample of 90 students at Belton High School, 80% of them are in favor of starting school
early (before August 21st).
a) Calculate a 98% confidence interval for the true proportion of students at BHS who favor
starting school early.
Conditions
Random sample
np>10, n(1-p)>10
Population of BHS is greater than 900 students
pˆ 1  pˆ 
.8 .2 
CI  pˆ  InvNorm(.99)
 .8  2.326
n
90
1-PropZint
x  72
n  90
.702,.898
We are 98% confident that the true proportion of students at Belton High
School who are in favor of starting school early is between .70191 and .89809.
b)
The school administration believe that the percentage of students in the district who favor
starting school early is 75%, Does this indicate that the percentage of the students favoring
a start date at BHS is higher than the district?
p is the proportion of students who favor starting school early
H0 : p  .75
Ha : p  .75
  .05
1-PropZTest
pvalue = .1366
Since the p-value is greater than  we fail to reject H0 . There is not
sufficient evidence to suggest that the true proportion of students at
Newman Smith High School who are in favor of starting school early is
greater than 75%.
A
11) If a 95%confidence interval for p is (.6, .72), what conclusion can we draw if we test H 0
a)
b)
c)
D
reject H0
fail to reject H0
accept H0
a:
d) accept Ha
e) There is insufficient
information given to answer.
12) Given H0: p = .30, Ha: p < .30, if you conclude that the proportion is less than .30 when it is actually .27,
then
a) you have made a Type I error
b) you have made a Type II error
c) the result of you test was not significant
d)
you have drawn a correct conclusion
e)
you failed to reject the null hypothesis
p
13) The local news station reported that the 97% confidence interval for the proportion of council members
C
who are in favor of a new ordinance is (.45, .53). What does the phrase 97% confidence mean?
a)
b)
c)
d)
e)
97% of the ordinances are between .45 and .53
97% of the time the proportion of council members in favor are between .45 and .53
There is a 97% probability that the proportion of council members in favor are between .45 and .53
There is a 97% chance that the proportion of council members in favor are between .45 and .53
None of these are true.
A
14) By what factor (approximately) would the margin of error increase if we increase the confidence level
from 95% to 98%?
a) 0.37
d) 1.68
b) 0.98
e) 2.33
c) 1.19
C
15) Light bulb manufacturer claims that less than 3% of its bulbs are defective. A consumer group decides
to test this hypothesis at the 5% level of significance. Which of the following is not an appropriate
interpretation of the 5% level of significance?
a) 5% is the probability of a Type I error
b) 5% is the probability of rejecting the null hypothesis when it’s true
c)
5% is the probability of accepting the null hypothesis when it’s false
d)
5% is the criteria for judging whether the sample statistic is sufficiently extreme to cast doubt on
the manufacturer’s claim
None of these is an appropriate interpretation
e)
16) Which of the following best describe a Type I error for a hypothesis test?
a)
It is the probability of accepting H0 when H0 is false.
b)
c)
d)
e)
It is the probability of rejecting H0 when H0 is true.
It is the complement of the power of the test.
It is the complement of a Type II error.
None of these describes a Type I error.
17) A hypothesis test on a null hypothesis of p0 =.5 is conducted at the 5% level of significance. The value
of β is calculated and found to be 0.12 for the alternative hypothesis of pa = .57. Which of the
following statements about β is false?
a) β is the probability of failing to reject H0 when H0 is false.
b) The power of the test is 0.88.
c) β is the probability of a Type II error.
d)
β is the complement of the probability of a Type I error.
e)
β would decrease for an alternative hypothesis pa = .59
18) When leaving for school on an overcast morning, you make a judgment on the null hypothesis: the
weather will remain dry. What would the results be of Type I and Type II errors?
a)
Type I error: get drenched. Type II error: needlessly carry an umbrella
b)
c)
Type I error:
Type I error:
dry
Type I error:
Type I error:
d)
e)
needlessly carry an umbrella. Type II error: get drenched
carry an umbrella & it rains. Type II error: carry no umbrella, but weather remains
get drenched. Type II error: carry no umbrella, but weather remains dry
get drenched. Type II error: carry an umbrella, and it rains