1)
At a local high school, 35% of the students play a sport. Of
those who play a sport, 80% are on the honor roll. Of the students
who do not play a sport, 60% are on the honor roll. If a student
was selected at random from this school, what is the probability
that the student plays a sport and is on the honor roll?
0.20
0.28
0.39
0.40
0.95
2)
A biologist is testing soil samples for the presence of a
certain type of pest. Each soil sample has 3 independent tests done
to check for the presence of the pest. The sample is clear if all
three tests come back negative. If, in reality, 90% of all tests
show an accurate negative outcome, what is the probability that a
soil sample will not be cleared?
0.001
0.081
0.243
0.271
0.729
3)
Let the random variable X represent the
number of toothbrushes owned by randomly chosen US adults. The
table below shows the probability distribution if the few adults
who own more than four toothbrushes is ignored.
What is the probability that a randomly selected US adult owns
at least two toothbrushes?
0.10
0.19
0.39
0.42
0.61
4)
Let X be the number of times a randomly
chosen high school student eats dinner with the family in one week.
The table below shows the probability distribution
of X.
What is the mean (expected value) of the number of dinners high
school students eat with their families?
1.05
3.5
3.95
4
7.05
5)
A certain store sells only sunglasses. Let the random
variable x represent the number of sunglasses
bought from the store on any day with mean 29 and standard
deviation 11. Let the random variable y be the
total revenue from this store on a randomly selected day. If
the store charges $100 per pair of sunglasses, what are the mean
and standard deviation of y?
= $29 and =
$11
= $29 and =
$1,100
= $2,900 and =
$11
= $2,900 and =
$1,100
= $2,900 and =
$12,100
6)
A local high school teacher wants to collect a simple random
sample of students at his school and use an 80% confidence interval
to estimate the proportion of students at this school who have worn
braces to straighten their teeth.
Of the following, which is the smallest sample size that will
result in a margin of error of no more than 5 percentage
points?
105
164
271
385
664
7)
A manager at a surf shop would like to know whether the majority
of surfers ride with their left foot first. A simple random sample
of 50 customers was taken, and of the 50, 29 say they surf with
their left foot first. A significance test is performed using the
hypotheses H0: p = 0.5
and Ha: p > 0.5,
which results in a P-value of 0.129. Which of the
following statements correctly interprets the P-value
of the test?
There is a 12.9% chance that p =
0.5.
There is a 12.9% chance that p =
0.58.
There is a 12.9% chance that a majority of surfers ride with
their left foot first.
If samples like these were to be taken many, many times, about
12.9% of those samples would result in the majority of surfers
riding with their left foot first.
If the proportion of surfers riding with their left foot first
really was at 50%, there is a 0.129 probability that the sample of
50 obtained would result in 29 or more who ride with their left
foot first.
8)
Alice did a study on the proportion of honeybees that survive
the winters of Alaska. She was criticized as lacking sufficient
statistical power. Which of the following would help to increase
the statistical power of Alice’s study?
Raise the significance level from 0.05 to 0.10.
Lower the significance level from 0.05 to 0.025.
Perform a two-tailed test instead of a one-tailed test.
Construct a confidence interval instead of a hypothesis
test.
Perform the study again, but this time with a smaller sample
size.
9)
The manager of a roofing company has two roofers, Alex and Brad.
The manager wants to estimate the difference in average number of
hours it takes to complete a job between these two workers. He
takes a random sample of 31 jobs that Alex has completed and finds
the mean number of hours is 16.7 with a standard deviation of 4.9.
The random sample of 35 jobs that Brad has completed yields a mean
of 20.6 hours with a standard deviation of 9.1 hours.
Which is the 95% confidence interval for the difference (Alex –
Brad) in mean number of hours to complete a roofing job?
10)
A group of factory workers volunteered to participate in a study
investigating the effect that listening to music has on fine motor
tasks. Each employee was assigned to each of two treatments:
listening to music while working, and no music while working. The
subjects are asked to assemble as many parts as they can in one
hour. The order of the treatments is assigned to each subject at
random.
A 95% confidence interval for the mean difference in parts
assembled (Music – No Music) is (1.37, 4.46). Based on this
interval, should the researchers conclude that factory workers like
the ones in this study assemble the same number of parts while
listening to music as not listening to music, on average?
Yes, because the confidence interval contains only positive
values.
Yes, because one subject assembled fewer parts when listening to
music than when they were not.
Yes, because one subject assembled the same number of parts when
listening to music than when they were not.
No, because almost all of the subjects assembled more parts when
listening to music than when they were not.
No, because the confidence interval does not contain 0; there is
evidence of a difference in part-assembling abilities.
11)
Administrators at a large university claim that the mean number
of students who visit the library daily is 705. A statistics class
at this university feels this claim is high, and
a t-test is performed on versus ,
where is
the true mean number of students who visit the library daily at
this university. The resulting P-value is 0.063. What
conclusion is to be made at the level?
The class failed to obtain any evidence
for Ha.
The class can accept H0 at the 5%
significance level.
The class can accept H0 at the 10%
significance level.
There is convincing evidence
against H0 in favor
of Ha.
At the 10% significance level, the class has proven
that Ha is true.
12)
The manufacturers of a new tablet claim their product lasts
longer on one charge than the typical tablet, which is 12 hours. A
hypothesis test is performed on versus .
Which of the following describes a Type II error in this
scenario?
concluding that the new tablets will boot up faster, when they
actually will not
concluding that the new tablets last longer than 12 hours on one
charge, when they actually do
concluding that the new tablets last longer than 12 hours on one
charge, when they actually do not
concluding that the new tablets do not last longer than 12 hours
on one charge, when they actually do
concluding that the new tablets do not last longer than 12 hours
on one charge, when they actually do not
13)
The length of baseball games varies from league to league.
Stephen wonders if there is a difference in the length of baseball
games between two leagues, A and B. He takes a random sample of 35
baseball games from League A and finds the mean length is 2.58
hours with a standard deviation of 0.52 hours. He then takes a
random sample of 28 baseball games from League B and finds the mean
length is 2.72 hours with a standard deviation of 0.39 hours. What
is the appropriate statistical test for analyzing the results?
paired t-test for a mean difference
one-sample z-test for a population mean
two-sample t-test for a difference in means
one-sample z-test for a population proportion
two-sample z-test for a difference in
proportions
14)
Producers of a fruit-flavored cereal claim the flavors follow
the distribution: 20% orange, 20% grape, 30% lemon, and 30% lime. A
statistics student wants to test this claim and counts the number
of flavors in one randomly selected box. She finds 135 orange
pieces, 163 grape pieces, 229 lemon pieces, and 244 lime
pieces.
What is the appropriate hypothesis test?
goodness
of fit test
test
for homogeneity
two-sample t-test for a difference in means
one-sample z-test for a population proportion