Texas A&M University
Department of Statistics
STAT 211: Principles of Statistics I
Practice Problems for Exam II, Fall 2023
Dr. Alexander Roitershtein
[Use the following information to answer the next 2 questions.]
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally
distributed with a mean of 527 and a standard deviation of 112.
1. What is the probability of a randomly selected candidate scoring above 500 on the GMAT?
Answer up to four decimal places.
a)
b)
c)
d)
e)
0.3682
0.4047
0.4836
0.5948
None of the other options.
2. How high must an applicant score on the GMAT in order to score in the highest 5%? Answer
up to two decimal places.
a)
b)
c)
d)
e)
705.22
707.22
709.22
711.22
713.22
3. Suppose Alice just found out that she scored 75 on her first Statistics exam, with a z-score of
−0.25. Her friend, Bob, who is in a different section with the same Professor, also scored 75 but
had a z-score of 0.35. What can you conclude about the mean exam scores in the classes?
a)
b)
c)
d)
e)
The mean exam scores of both classes must both be equal to 75.
The Alice’s class had a lower mean score compared to Bob’s class.
The Alice’s class had a higher mean score compared Bob’s class.
It is impossible to say without seeing all of the individual test scores.
It is impossible to say since we don’t know the shape of either distribution.
1
[Use the following information to answer the next 3 questions.]
A researcher is interested in the amount of water Texans drink per day on average. The true
amount of water that Texans drink on any given day is normally distributed with a mean of 3,400
ml and a standard deviation of 400 ml. The researcher takes a random sample of 16 Texans and
records how much water they drank in the previous 24 hours.
4. What is the distribution of the average amount of water drunk by the participants in a random
sample of 16 Texans?
a) X̄ ∼ N µX̄ = 3400, σX̄ = 400
q
(400/3400)(3000/3400)
400
b) p̂ ∼ N µp̂ = 3400 , σp̂ =
16
400
c) X̄ ∼ N µX̄ = 3400, σX̄ = √
16
q
(3000/3400)(400/3400)
d) p̂ ∼ N µp̂ = 3000
,
σ
=
p̂
3400
16
e) None of the other options
5. Using the Empirical Rule calculate the probability that the sample mean is greater than
3700 ml.
a)
b)
c)
d)
e)
0.9970
0.0015
0.7743
0.2257
0.0030
6. The researcher constructs a 95% confidence interval for the parameter of interest. If we were
to quadruple the sample size to 64 Texans, how would the width of the confidence interval change?
a)
b)
c)
d)
e)
The new confidence interval will be two times wider than the previous confidence interval.
The new confidence interval will be four times wider than the previous confidence interval.
The previous confidence interval will be two times wider than the new confidence interval.
The previous confidence interval will be four times wider than the new confidence interval.
These two confidence intervals will be equal in size since the error bound remains unaltered.
2
7.
The number of calories consumed per day is a question of interest for nutritionists. It is
known from past studies that the standard deviation of calories per day is 250. Nutritionists want
to construct a 95% confidence interval for the amount of calories consumed per day, but sampling
is expensive and they want to save money. What is the minimum sample size needed to create a
95% confidence interval such that the width is 100?
a)
b)
c)
d)
e)
384
385
96
97
None of the other options
8.
A political candidate, Alice, is running for office and she wants to know what her approval rating is and has hired you to help. You decided to take a sample of 100 people in
the town and find that 64 of the people you sampled approve of Alice. Which of the intervals
is the correct 99% confidence interval for Alice’s approval rating? Answer up to four decimal figures.
a)
b)
c)
d)
e)
(0.5167, 0.7634)
(0.2367, 0.4834)
(0.5459, 0.7341)
(0.2659, 0.4541)
None of the other options
9. A utility company wants to know the average electricity used per residential customer per day.
A random sample of 41 residential customers are taken with sample mean of 30 kWh and sample
standard deviation of 4.3 kWh, assume the population is approximately normally distributed.
Which expression is the correct margin of error for a 90% confidence interval of the parameter of
interest? Choose the nearest option.
a) 1.96 ∗
4.3
√
41
b) 1.64 ∗
4.3
√
41
c) 2.02 ∗
4.3
√
41
d) 1.68 ∗
4.3
√
41
e) None of the other options
3
10.
An inspector inspects a shipment of medications to determine the efficacy in terms of
the proportion p in the shipment that failed to retain full potency after 60 days of production.
Unless there is clear evidence that this proportion is significantly less than 0.05, she will reject the
shipment. To reach a decision she selects a simple random sample of 200 pills. Suppose that 8 of
the pills have failed to retain their full potency. What is the standard error of the sample mean?
Answer up to three decimal places.
a)
b)
c)
d)
e)
0.001
0.014
0.024
0.069
None of the above
[Use the following information to answer the next 2 questions.]
Medical researchers now believe there may be a link between baldness and heart attacks in men.
The hypothesis testing problem that we’re interested in is
H0 : There is no link between baldness and heart attacks in men
vs
Ha : There is a link between baldness and heart attacks in men
at level of significance α = 0.05.
11.
What would constitute a Type II error in this study?
a) The study finds no link between baldness and heart attacks in men when in reality there is
no link between baldness and heart attacks in men.
b) The study finds a link between baldness and heart attacks in men when in reality there is no
link between baldness and heart attacks in men.
c) The study finds no link between baldness and heart attacks in men, when in reality there is
a link between baldness and heart attacks in men.
d) The study finds a link between baldness and heart attacks in men, when in reality there is a
link between baldness and heart attacks in men.
12.
a)
b)
c)
d)
e)
What is the probability the test will result in a Type I error?
0.05
0.95
0.01
0.99
0.025
4
[Use the following information to answer the next 2 questions.]
Suppose you roll a fair die 64 times where each roll is independent. A success in each trial is
defined as getting a 4 or more. You are interested in the number of successes you get in 64 trials.
13.
a)
b)
c)
d)
e)
14.
a)
b)
c)
d)
e)
What is the appropriate distribution?
Normal(µ = 64/3, σ = 2/3)
Normal(µ = 32, σ = 8)
Normal(µ = 16, σ = 4)
Binomial(n = 64, p = 1/4)
Binomial(n = 64, p = 1/2)
Find the mean and standard deviation of the above distribution.
mean=32,
mean=64,
mean=32,
mean=64,
mean=16,
standard
standard
standard
standard
standard
deviation=4
deviation=4
deviation=8
deviation=8
deviation=8
15. The STAT201 Exam 2 scores are normally distributed and their middle 68% scores are
between 60 and 86. Calculate the approximate mean and standard deviation of the distribution.
Hint: Use the Empirical rule.
a)
b)
c)
d)
e)
µ = 70 and σ = 6.5
µ = 73 and σ = 6.5
µ = 70 and σ = 13
µ = 73 and σ = 13
µ = 0 and σ = 1
16. The SAT scores are normally distributed with mean 1,500 and standard deviation 300, and
the ACT scores are also normally distributed with mean 21 and standard deviation 5. Jeff earned
1,800 on his SAT and Jane earned 24 on her ACT. A college admissions officer wants to determine
which of the two applicants scored better on their standardized test with respect to the other test
takers. Choose the correct explanation.
a) Jeff scored higher on his standardized test with respect to the other test takers than Jane
did.
b) Jane scored higher on her standardized test with respect to the other test takers than Jeff
did.
c) Jeff and Jane scored the same on their standardized tests with respect to the other test takers.
d) The admission officer is unable to compare their scores because the SAT and ACT have
different distributions.
e) None of the above
5
[Use the following information to answer the next 2 questions.]
According to the US Census Bureau’s American Community Survey, 87% of Americans over the
age of 25 have earned a high school diploma. Suppose a simple random sample of size n = 100
from this population has been drawn.
17. Compute the mean and the standard deviation of the proportion of Americans in the sample
who have a high school diploma.
a)
b)
c)
d)
e)
µp̂
µp̂
µp̂
µp̂
µp̂
= 0.87,
= 0.13,
= 0.87,
= 0.13,
= 0.87,
σp̂
σp̂
σp̂
σp̂
σp̂
= 0.0113
= 0.0113
= 0.0336
= 0.0336
= 0.00336
18. What is the probability that the percentage of Americans in the sample with a high school
diploma is less than 85%? Answer up to four decimal places.
a)
b)
c)
d)
e)
0.0385
0.1862
0.2760
0.3746
0.7240
19. The American Community Survey (ACS), part of the United States Census Bureau, conducts a
yearly census similar to the one taken every ten years, but with a smaller percentage of participants.
The most recent survey estimates with 90% confidence that the mean household income in the U.S.
falls between $69,720 and $69,922. Find the point estimate for mean U.S household income and
the error bound or the margin of error (MoE) for mean U.S. household income.
a)
b)
c)
d)
e)
Point
Point
Point
Point
Point
estimate = 69000; MoE = 100
estimate = 69800; MoE = 101
estimate = 69821; MoE = 101
estimate = 69821; MoE = 202
estimate = 69842; MoE = 101
[Use the following information to answer the next 4 questions.]
Assume that the population distribution of bag weights is normal with an unknown population
mean and a known standard deviation of 0.1 ounces. A random sample of 16 small bags of the
same brand of candies was selected. The weight of each bag was then recorded. The mean weight
of the bags in the sample was 2.5 ounces. Suppose we wish to construct a 95% confidence interval
for the mean weight of bags of that specific brand of candies.
6
20. What formula would you use to construct a 95% confidence interval for the mean weight of
bags? The symbols bear their usual meanings.
a) X̄ ± z ∗ × √Sn , where z ∗ = 1.96
b) X̄ ± z ∗ × √σn , where z ∗ = 1.96
c) X̄ ± t∗15 × √σn , where t∗15 = 2.131
d) X̄ ± t∗15 × √Sn , where t∗15 = 2.131
e) None of the above. The conditions for the confidence interval are not satisfied.
21. Consider the following interpretations of a 95% confidence interval for the mean weight of
bags in this context.
(I) If we take 10, 000 repeated samples under identical conditions, then in approximately 9, 500
cases, the population mean weight of bags would be equal to 2.5 ounces.
(II) If we take 10, 000 repeated samples under identical conditions, then approximately 9, 500 of
the estimated confidence intervals calculated from those samples will contain the population
mean weight of bags.
(III) If we take 10, 000 repeated samples under identical conditions, then in approximately 9, 500
cases, the estimated confidence intervals calculated from those samples would contain the
sample mean weight of 2.5 ounces.
(IV) If we take 10, 000 repeated samples under identical conditions, then approximately 500 of the
estimated confidence intervals calculated from those samples will not contain the population
mean weight of bags.
(V) There is a 95% probability that the sample mean weight of bags will lie within the confidence
interval.
Select the correct answer from the following options:
a)
b)
c)
d)
e)
(II) is true.
(I) and (II) are true.
(I) and (III) are true.
(II) and (IV) are true.
(I), (II), and (V) are true.
22.
What change, if any, would you observe in the 95% confidence interval if we use another
random sample of size n = 64 instead of n = 16?
a) The new confidence interval will be two times wider than the previous confidence interval.
b) The new confidence interval will be four times wider than the previous confidence interval.
c) The new confidence interval will be two times narrower than the previous confidence
interval.
d) The new confidence interval will be four times narrower than the previous confidence
interval.
e) These two confidence intervals will have an equal width since the error bound remains unaltered.
7
23. Suppose, instead of a 95% interval, we wish to construct a 90% confidence interval for the
mean weight of bags. In that case, find the minimum sample size in order to ensure that the
width of the 90% confidence interval is no larger than 0.1.
a)
b)
c)
d)
e)
10
11
15
16
27
24. The owner of a travel agency would like to determine whether or not the mean age of the
agency’s customers is over 24. If so, he plans to alter the destination of their special cruises and
tours. If he concludes the mean age is over 24 when it is actually not, he makes a ( ) error. If he
concludes the mean age is not over 24 when it actually is, he makes a ( ) error.
a) Type II, Type I
b) Type I, Type II
c) Type I, Type I
d) Type II, Type I
e) α, Power
25.
The Nielson Company reported that nationally 30% of Millennials order groceries online.
Suppose that a U.S. grocery company wishes to test whether this figure is different in their local
market. The test will be conducted at the 1% significance level. What is the probability that the
grocery company will commit a Type I error?
a) 0.01 α = Pr(type I error)
b) 0.02
c) 0.05
d) 0.10
e) Not enough information
26. You are planning to use a sample proportion p̂ to estimate a population proportion p. Suppose
a sample size of n = 100 and a confidence level of 95% yielded a margin of error of 0.025. Which
of the following will result in a larger margin of error?
(I) Increasing the sample size while keeping the same confidence level
(II) Decreasing the sample size while keeping the same confidence level
(III) Increasing the confidence level while keeping the same sample size
(IV) Decreasing the confidence level while keeping the same sample size
a)
b)
c)
d)
e)
I and III
I and IV
II and III
II and IV
None of the above
8
27. Suppose we are testing the hypotheses H0 : µ = 70 vs Ha : µ > 70. Of the following sample
means, which one will have the largest P-value? (Hint: draw a sampling distribution of X̄.
a) x̄ = 72
b) x̄ = 70
c) x̄ = 68
d) x̄ = 66
e) x̄ = 60
28.
Out of 2000 students in the school, 1400 passed an exam. What is approximately the
standard error of p̂?
a)
b)
c)
d)
0.0001
0.0094
0.0078
0.9999
[Use the following information to answer the next 2 questions.]
The proportion of a population with a characteristic of interest is p = 0.63.
29.
Find the mean and standard deviation of the sample proportion p̂ obtained from random
samples of size 3, 600.
a)
b)
c)
d)
30.
a)
b)
c)
d)
e)
µp̂
µp̂
µp̂
µp̂
= 0.63,
= 0.37,
= 0.37,
= 0.63,
σp̂
σp̂
σp̂
σp̂
= 0.008.
= 0.08.
= 0.008.
= 0.08.
How will the standard deviation of p̂ change if you decrease the size of the sample?
decreases
remains the same
increases
depends on the distribution
None of the other options
31.
It is known that 5-year stomach cancer survival rate is 63%. 100 patients with stomach
cancer were randomly selected and it is found that the survival rate is 57% after 5 years.Assume
that many random samples of size 100 patients are drawn and the sampling distribution of sample
proportion is obtained. Which of the following is TRUE?
a)
b)
c)
d)
e)
It
It
It
It
It
is
is
is
is
is
exactly normal with mean 0.57 and standard deviation 0.0495.
a binomial distribution with n = 100 and p = 0:63
approximately normal with mean 0.63 and standard deviation 0.0483.
exactly normal with mean 0.63 and standard deviation 0.0483.
approximately normal with mean 0.57 and standard deviation 0.0495.
9
[Use the following information to answer the next 5 questions.]
Peggy is interested in the mean height of young women aged 18 to 24 in the US. Assume the
population standard deviation is known to be 2.5 inches. She takes a sample of 72 young women
aged 18 to 24 in the US and calculates a sample mean of 65 inches.
32.
a)
b)
c)
d)
What is the parameter of interest?
The
The
The
The
mean
mean
mean
mean
height
height
height
height
of
of
of
of
the 72 young women aged 18 to 24 in the US
young women aged 18 to 24 in the US
young women aged 18 to 24 in the world
the 72 young women aged 18 to 24 in the world
33. Assume Peggy wants to create a 95% confidence interval about the true parameter. Which
interpretation of a 95% confidence interval is correct?
a) If we took repeated samples, the sample mean would equal the population mean in approximately 95% of the samples.
b) If we took repeated samples, approximately 95% of the confidence intervals calculated from
those samples would contain the sample mean of 65
c) If we took repeated samples , approximately 95% of the confidence intervals calculated from
those samples would contain the true parameter
d) There is a 95% probability that the true parameter is included within the interval
e) There is a 95% probability that the sample mean of 65 is included within the interval
34. Assume Peggy wants to create a 95% confidence interval about the true parameter. What is
the margin of error or error bound?
a)
b)
c)
d)
e)
35.
a)
b)
c)
d)
36.
a)
b)
c)
d)
0.29
0.34
0.58
0.68
Not enough information provided to answer this question
What will happen to the margin of error if the confidence level is now 90% instead of 95%?
The margin
The margin
The margin
Not enough
of error will decrease
of error will increase
of error will be the same
information provided to answer this question
What will happen to the margin of error if the sample size is now 36 instead of 72?
The margin
The margin
The margin
Not enough
of error will decrease
of error will increase
of error will be the same
information provided to answer this question
10
[Use the following information to answer the next 4 questions.]
Suppose a random sample of size n = 80 is drawn from a normal population with an unknown mean
µ and a known standard deviation 2. Let (2.19, 3.67) be a 95% confidence interval for µ based on
the observed sample and the sample standard deviation is 2.67.
37. Find the sample mean.
a)
b)
c)
d)
e)
3.67
2.19
2.67
2.93
1.48
38. Find the corresponding margin of error.
a)
b)
c)
d)
e)
0.05
0.72
0.74
0.76
1.48
39. Now suppose we wish to construct a 98% confidence interval based on a new sample while keeping the margin of error unaltered. Which of the following statements do you think would be correct?
a)
b)
c)
d)
We need to decrease the sample size n.
We need to increase the sample size n.
Sample size n does not have any effect on the margin of error.
Sample size n should remain the same to obtain the same margin of error.
40. Further, suppose we wish to construct a new confidence interval based on a new sample of
size n = 30 while keeping the margin of error unaltered. Which of the following statements do you
think would be correct?
a)
b)
c)
d)
We need to decrease the level of confidence.
We need to increase the level of confidence.
Level of confidence should remain the same to obtain the same margin of error.
Level of confidence does not have any effect on the margin of error.
41. Peggy is interested in the mean height of young women aged 18 to 24 in the US. Assume the
population standard deviation is known to be 2.5 inches. What would be the minimum sample
size required so that the width of a 95% confidence interval does not exceed 1 inch?
a)
b)
c)
d)
e)
85
89
93
97
100
11
42. Gallup took in 2013 a nationally representative sample of 2027 adults and asked them about
their soda consumption. The survey shows that 24% mostly drink diet soda. Based on the results,
a 95% confidence interval for the proportion of American adults who mostly drink
diet soda is:
a)
b)
c)
d)
e)
0.24 ± 0.018
0.24 ± 0.009
0.24 ± 1.96
0.24 ± 0.152
0.24 ± 0.95
43. Earlier this month, 50% Californians voted ‘yes’ on Measure H: a sales tax measure to fund
homeless services and prevention. They took a sample of 50 Californians. Find the 80th percentile
for the above distribution of sample proportions.
a)
b)
c)
d)
e)
0.56
0.64
0.66
0.50
0.059
[Use the following information to answer the next 3 questions.]
A New Research Center poll included 1500 randomly selected adults who were asked whether “global
warming is a problem that requires immediate government action”. Results showed that 850 of
those surveyed indicated that immediate government action is required. Let p = the population
proportion of adults who believe that immediate government action is required.
44.
a)
b)
c)
d)
e)
A 95% confidence interval for p is given by
0.57 ± 0.025
0.57 ± 0.033
0.57 ± 0.021
0.57 ± 0.020
0.57 ± 0.035
45.
Another researcher Samantha requests to see a 85% confidence interval based on the
same data. Pick the correct option.
a)
b)
c)
d)
e)
The 95% interval will be wider than the 85% interval
The 95% interval will be approximately the same as the 85% interval
The 95% interval will be narrower than the 85% interval
Cannot compare the 95% and 85% intervals without looking at the data
More information is required
12
46. Peter decides to estimate the above parameter by making a 90% confidence interval. What
could he do to reduce the margin of error?
a)
b)
c)
d)
e)
Increase the number of students in his sample
Decrease the number of students in his sample
Use a different sampling scheme
He must consider a different sample of 1500 adults
None of the above
[Use the following information to answer the next 3 questions.]
Answer the next three questions based on the following information. The university is interested
to know whether the students support sport passes to be included in their tuition fees. 250
students are sampled to estimate the proportion of students who support sports passes being
included in tuition. Of them, 133 support it and 117 oppose.
47.
a)
b)
c)
d)
Find a 99% confidence interval for the proportion.
(0.469,0.595)
(0.451,0.613)
(0.421,0.643)
(0.350,0.586)
48. The university president wants to know if more than half of the students support sport passes
being included in the tuition fee. The sample proportion was 0.52. What would the appropriate
null and alternative hypothesis be in this case?
a)
b)
c)
d)
H0
H0
H0
H0
: p = 0.5 vs. Ha : p > 0.5
: p = 0.5 vs. Ha : p ̸= 0.5
: p = 0.52 vs. Ha : p > 0.52
: p̂ = 0.52 vs. Ha : p̂ > 0.52
49. The above hypothesis test is conducted. The p–value is 0.04 and the sample proportion was
0.52. What is the correct interpretation of this p–value?
a) There is a 0.04 probability that the population proportion is 0.52.
b) The true proportion must be bigger than 0.5.
c) If hypothesis tests are conducted based on repeated samples, approximately 4% of these
samples would have sample means away from the hypothesized value of 0.5.
d) There is a 0.04 probability that the null hypothesis is correct.
13
50.
Assume that a full survey is conducted and the true population proportion is 0.53. If a
sample of 200 individuals is taken what is the expected value of the number of people who support
the measure and the standard deviation of that estimate.
a)
b)
c)
d)
expected
expected
expected
expected
value:
value:
value:
value:
106, standard deviation: 7.058
106, standard deviation: 49.82
53, standard deviation: 49.82
53, standard deviation: 7.058
51.
A researcher conducted an experiment on 8 randomly selected NASCAR drivers in which
their reaction time was measured. The sample mean reaction time was 1.24 secs. The sample
standard deviation reaction time was 0.12 secs. Assume that reaction time follows a normal
distribution, construct the 98% confidence interval for the population mean reaction time based
on these data is given by:
a)
b)
c)
d)
e)
1.24 ± 0.083
1.24 ± 0.099
1.24 ± 0.118
1.24 ± 0.127
1.24 ± 0.136
52.
Suppose the mean speed of internet in your apartment is usually 35 MBps. The internet
provider, Sudden-Link, charged you more for the last month. They claimed the mean speed of
your internet connection to be more than 35 MBps. You are skeptical. So you tracked your daily
internet speed for the last 30 days. Your speed data yields the sample mean 36.2 and the sample
standard deviation 4.32. Suppose the Sudden-Link manager asked you to provide a 95% confidence
interval for the true mean speed of the Internet based on your sample. What should be your answer?
4.32
√
30
4.32
36.2 ± t0.025;29 × √
30
4.32
36.2 ± z0.05 × √
30
4.32
36.2 ± z0.025 × √
30
4.32
35 ± t0.025;29 × √
30
a) 36.2 ± t0.05;29 ×
b)
c)
d)
e)
53.
The Dallas Cowboys may be first in the NFC East, but they are in a 6 − 6 position this
season. Suppose a survey was conducted on the proportion of Cowboys fans who believe Jason
Garrett should be fired and the 95% confidence interval is (0.73, 0.96). How would you interpret
this in context?
a) We are 95% confident that the true mean number of people who believe Jason Garrett
should be fired is between 0.73 and 0.96.
b) We are 90% confident that the true mean number of Cowboys fans who believe Jason
Garrett should not be fired is between 0.73 and 0.96.
c) We are 95% confident that the true proportion of Cowboys fans who believe Jason Garrett
should be fired is between 0.73 and 0.96.
d) We are 95% confident that the true proportion of people who believe Jason Garrett should
be fired is between 0.73 and 0.96.
14
54. According to the American Automobile Association (AAA), erroneous driving is the cause of
approximately 54% of all fatal automobile accidents in US. Thirty randomly selected fatal accidents
are examined, and it is found that 14 of them were due to driving error. Suppose the typical mean
height of the population is 64 inches, and Laura suspects that the mean height might be greater
than 64 inches. What should be her null and alternative hypotheses?
a) H0 : µ = 64 vs Ha : µ > 64
b) H0 : µ ≥ 64 vs Ha : µ < 64
c) H0 : X = 64 vs Ha : X > 64
d) H0 : X > 64 vs Ha : X ≤ 64
55. When a new drug is created, the pharmaceutical company must subject it to testing before
receiving the necessary permission from the Food and Drug Administration (FDA) to market the
drug. Suppose the null hypothesis is ”the drug is unsafe.”
What is the Type II Error?
a)
b)
c)
d)
To
To
To
To
conclude
conclude
conclude
conclude
the
the
the
the
drug
drug
drug
drug
is
is
is
is
safe when in, fact, it is unsafe.
unsafe when, in fact, it is safe.
safe when, in fact, it is safe.
unsafe when, in fact, it is unsafe.
56. In testing H0 : µ = 5 vs. Ha : µ > 5, a sample of size n = 50 yielded a p-value of 0.014.
If α = 0.01, and the true value of the mean was actually µ = 7, then the decision based on the data:
a)
b)
c)
d)
e)
was a Type I error.
was a Type II error.
was correct.
was powerful.
cannot be determined.
57. In testing H0 : p = 0.5 vs. Ha : p < 0.5, a sample of size n = 100 yielded a p-value of 0.027.
If α = 0.05, and the true value of the population proportion p was actually p = 0.38, then the
decision based on the data:
a)
b)
c)
d)
e)
was a Type I error.
was a Type II error.
was correct.
was powerful.
cannot be determined.
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58. A group of doctors is deciding whether or not to perform an operation to remove a cancerous
tumor. Suppose the null hypothesis is: H0 : the surgical procedure will successfully remove the
tumor. State the Type I and Type II errors in complete sentences.
a) T1: In reality, the surgery went well but the doctors want to operate again. They think they
did not remove the tumor. T2: The doctors think they got all of the tumors when in reality
they failed to get it all and you still have cancer.
b) T1: The doctors think they got all of the tumors when in reality they failed to get it all and
you still have cancer. T2: In reality, the surgery went well but the doctors want to operate
again. They think they did not remove the tumor.
c) T1: In reality, the surgery went well and the doctors think you are better. T2: The doctors
think they got all of the tumors when in reality they failed to get it all and you still have cancer.
d) T1: In reality, the surgery went well but the doctors want to operate again. They think they
did not remove the tumor. T2: The doctors think they failed to get all of the tumors when
in reality they failed to get it all and you still have cancer.
16