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WorksheetsAP Statistics Review
Total questions: 21
Worksheet time: 2hrs 41mins
Name
Class
Date
1.
A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses?
a)
996
b)
998
c)
1000
d)
1002
2.
A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or a 6?
a)
2/3
b)
1/2
c)
3/8
d)
1/3
3.
You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red?
a)
0.1551
b)
0.1600
c)
0.2222
d)
0.4444
4.
A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5000 with probability 9/20, to break even with probability 5/20, and lose $5000 with probability 3/20. The expected profit in dollars is
a)
1500
b)
0
c)
3000
d)
3250
5.
Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown that X is approximately Normally distributed with a mean of 250 pounds and a standard deviation of 50 pounds. What is P(X > 325 pounds)?
a)
0.0668
b)
0.2514
c)
0.7486
d)
0.8531
6.
Songs on Leila's smartphone have a mean length of 4.3 minutes and a standard deviation of 1.2 minutes. The phone inserts a period of silence between songs that has a length of 0.2 minutes and a standard deviation of 0.1 minutes. What are the mean and standard deviation of time it takes for the phone to play a randomly selected two-song sequence?
a)
Mean = 4.5 min.; SD = 2.5
b)
Mean = 8.8 min.; SD = 2.5
c)
Mean 4.5 min.; SD = 1.7
d)
Mean = 8.8 min.; SD = 1.7
7.
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of the trees show some signs of damage. Which of the following statements is correct?
a)
40% is a parameter
b)
40% is a statistic
c)
40% of all trees in the forest show some signs of damage
d)
More than 40% of the trees in the forest show some signs of damage
8.
The sampling distribution of a statistic is
a)
the probability that we obtain the statistic in repeated random samples.
b)
the mechanism that determines whether randomization was effective.
c)
the distribution of values taken by a statistic in all possible samples of the same sample size from the same population.
d)
the extent to which the sample results differ systematically from the truth.
9.
A statistic is said to be unbiased if
a)
the survey used to obtain the statistic was designed so as to avoid even the hint of a racial or sexual prejudice.
b)
the mean of its sampling distribution is equal to the true value of the parameter being estimated.
c)
both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful.
d)
the value of the statistic from any sample is equal to the parameter being estimated.
10.
The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that
a)
as we look at more and more bulbs, their mean burnout time gets ever closer to the mean mu for all bulbs of this type.
b)
the mean burnout time for any number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs.
c)
the mean burnout time for any number of bulbs has a distribution that is close to Normal
d)
the mean burnout time for a large number of bulbs has a distribution that is close to Normal
11.
You take a SRS of size 500 from the 37,000 students at Purdue University and measure individual's heights. You then take an SRS of size 500 from the 4,400,000 adults in the state of Indiana and measure their heights. Assuming the standard deviation of individual heights in the two populations is the same, the standard deviation of the sampling distribution of mean heights for the Indiana sample is
a)
approximately the same as for the Purdue sample because both are samples of size 500.
b)
smaller than for the Purdue sample because the population of Indiana is much larger.
c)
larger than for the Purdue sample because the population of Indiana is much larger.
d)
larger, because the Indiana sample is smaller relative to the population from which it's been taken.
12.
In an opinion poll 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately
a)
0.0094
b)
0.0306
c)
0.0353
d)
0.2500
13.
A traffic consultant wants to estimate the proportion of cars on a certain street that have more than two occupants. She stands at the side of the road for two hours on a weekday afternoon and flips a coin each time a car approaches. If the coin comes up heads, she counts the number of occupants in the car. After two hours, she has counted 103 cars, 15 of which had more than two occupants. Which condition for constructing a confidence interval for a proportion has he failed to satisfy?
a)
n ≥ 30
b)
np ≥ 10
c)
The sample is less than 10% of the population.
d)
The data is an SRS from the population of interest.
14.
To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean x̄ of the weighings is computed. Suppose the scale readings are Normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of 0.0001?
a)
196
b)
27,061
c)
10,000
d)
38,416
15.
A 95% confidence interval for the mean reading achievement score for a population of third-grade student is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same data. Which of the following statements is correct?
a)
The interval is the same width.
b)
The 99% interval is narrower.
c)
the 99% interval is wider.
d)
The 99% interval could be wider or narrower--it depends on the sample.
16.
What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?
a)
0.90
b)
1.282
c)
1.397
d)
1.415
17.
The weights of 9 men have mean x̄ = 175 pounds and standard deviation s = 15 pounds. What is the standard error of the mean?
a)
58.3
b)
15
c)
5
d)
1.67
18.
In a test of H₀: p = 0.7 against Hₐ p ≠ 0.7, a sample of size 80 produces z = 0.8 for the value of the test statistic. Which of the following is closest to the P-value of the test?
a)
0.2090
b)
0.2119
c)
0.4238
d)
0.4681
19.
Because t procedures are robust, the most important condition for their use is
a)
the population standard deviation is known.
b)
the population distribution is approximately Normal.
c)
the data can be regarded as a random sample from the population.
d)
np and n(1 - p) are both at least 10.
20.
We want to test H₀: μ = 1.5 vs. Hₐ: μ ≠ 1.5 at α = 0.05. A 95% confidence interval for μ calculated from a given random sample is (1.4, 3.6). Based on this finding we
a)
fail to reject H₀.
b)
reject H₀.
c)
cannot make any decision at all because of the value of the test statistic is not available.
d)
cannot make any decision at all because the distribution of the population is unknown.
21.
All of us nonsmokers can rejoice -- the mosaic tobacco virus that affects and injures tobacco plants is spreading! Meanwhile, a tobacco company is investigating if a new treatment is effective in reducing the damage caused by the virus. Eleven plants were randomly chosen. On each plant, on leaf was randomly selected, and one half of the leaf (randomly chosen) was coated with the treatment, while the other half was left untouched (control). After two weeks, the amount of damage to each half of the leaf was assessed. For purposes of comparing the damage, which of the following is the appropriate type of procedure?
a)
Two-proportion z procedures
b)
Two-sample z procedures
c)
Matched pairs t procedures
d)
Two proportion t procedures
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