Mock Exam Midterm Statistics II, LBS summer term 2022
Dr Christian Reiner
1) If the significance level 𝛼 is 0.02, which p-value for a test statistic will result in a test
conclusion to reject H0?
A. 0.05
B. 0.01
C. 0.98
D. 0.97
E. 0.03
2) You’re conducting an experiment with 55 customers and you want to test the following
hypotheses: 𝐻0 : 𝜇 = 4 𝑣𝑠 𝐻𝑎 : 𝜇 ≠ 4. The standard error is 0.5, and the alpha level is
0.05. The population of values is normally distributed. Suppose that your test statistic is
1.42. What is the p-value interval for this result?
A. 0.005<p<0.01
B. 0.5<p<1.0
C. 0.2<p<0.4
D. 0.15<p<0.3
E. 0.1<p<0.2
3) Based on the following information, what is your conclusion? 𝐻0 : 𝜇 = 348 𝑣𝑠 𝐻𝑎 >
348, 𝛼 = 0.05 and p-value = 0.07
A. You should reject 𝛼.
B. You should fail to reject H0.
C. You should fail to reject 𝛼.
D. You should reject Ha.
E. You should accept H0.
4) If the alpha level is 0.05, what is the probability of a Type II error?
A. 0.05
B. impossible to tell without further information
C. 0.99
D. 0.95
E. 0.01
5) It’s believed that the average amount of sleep a person in the United States gets per
night is 6.3 hours. A mom believes that mothers get far less sleep than that. She contacts
a random sample of 20 other moms on a mom social networking site and finds that they
get an average of 5.2 hours of sleep per night, with a standard deviation of 1.8 hours.
Using this data, what is the value of the test statistic t from a t-test for a single
population mean?
A. –2.73
B. –2.66
C. 2.24
D. –12.11
E. 12.22
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6) In a company, employees type an average of 20 words per minute. Typing rates are
normally distributed with a standard deviation of 3. The manager of a large branch of the
company believes that his employees do better than that. He randomly samples 30
employees from his branch and finds an average typing rate of 20.5 words per minute. If
the manager wants a significance level of 0.05, what can he conclude?
A. Accept the null hypothesis that the average words per minute is equal to 20.
B. Reject the null hypothesis and conclude that the average words per minute is greater than
20.
C. Fail to reject the null hypothesis that the average words per minute is equal to 20.
D. Reject the null hypothesis that the average words per minute is equal to 20 and conclude
that it’s not equal to 20.
E. None of the above.
7) A magazine reports that the average number of minutes that U.S. teenagers spend
texting each day is 120. You believe it’s less than that. What are your null and alternative
hypotheses?
A. 𝐻0 : 𝜇 = 120 𝑣𝑠 𝐻𝑎 : 𝜇 ≠ 120
B. 𝐻0 : 𝜇 = 120 𝑣𝑠 𝐻𝑎 : 𝜇 < 120
C. 𝐻0 : 𝑥̅ = 120 𝑣𝑠 𝐻𝑎 : 𝑥̅ < 120
D. 𝐻0 : 𝑥̅ = 120 𝑣𝑠 𝐻𝑎 : 𝑥̅ ≠ 120
E. none of the above
8) A precocious child wants to know which of two brands of batteries tends to last longer.
She finds seven toys, each of which requires one battery. For each toy, she then
randomly chooses one of the brands, puts a fresh battery of that brand in the toy, turns
the toy on, and records the time before the battery dies. She repeats the experiment
with a battery of the brand not used in the first trial for each toy. Her data is listed in the
following table (in terms of hours of battery life before failure):
Assume that the difference scores are normally distributed. The sample standard deviation
of difference scores (sd) is 0.9214. At an alpha level of 0.01, given a not equal to alternative
hypothesis, what is (are) the critical value(s) of t?
A. -2.364; 2.364
B. -5.407; -5.407
C. 2.446
D. 3.499
E. -3.707; 3.707
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9) A psychologist read a claim that average intelligence differs between smokers and
nonsmokers and decided to investigate. She sampled 30 smokers and 30 nonsmokers
and gave them an IQ test. She used an alpha level of 0.10. The mean for the smokers is
51.9, and the mean for the nonsmokers is 52.6. The population variance for each group is
5.
Suppose that you were instead using an alpha level of 0.05. What would your decision be
regarding this data?
A. The null hypothesis can’t be rejected. This study doesn’t support the idea that smokers
and nonsmokers differ in IQ.
B. The null hypothesis can be rejected. Nonsmokers appear to be smarter than smokers.
C. The null hypothesis can’t be rejected, but the researcher can still say with confidence that
smokers are smarter than nonsmokers.
D. The null hypothesis can be rejected. Smokers do appear to be smarter than nonsmokers.
E. Accept the alternative hypothesis. Nonsmokers appear to be smarter than smokers.
10) You’re interested in the willingness of adult drivers (age 18 and over) in a metropolitan
area to pay a toll to travel on less-congested roads. You draw a sample of 100 adult
drivers and administer a survey on this topic to them.
One of your questions asks whether the respondent voted in the last election. You find a
much higher proportion of individuals claiming to have voted than is indicated by public
records. What is this an example of?
A. negativity bias
B. selection bias
C. non-response bias
D. response bias
E. undercoverage bias
11) You want to survey students at a high school and calculate the mean age. Which of the
following procedures will result in a simple random sample?
A. selecting one student at random, asking him or her to suggest three friends to participate
and continuing in this fashion until you have your sample size
B. using an alphabetized student roster and selecting every 15th name, starting with the first
one
C. numbering the students by using the school’s official roster and selecting the sample by
using a random number generator
D. classifying the students as male or female and drawing a random sample from each
E. selecting three tables at random from the cafeteria during lunch hour and asking the
students at those tables for their age
12) Which of the following is an example of a good census of 2,000 students in a high school?
A. calculating the mean age of all the students by using their official records
B. asking the first 25 students who arrive at school on a given day their age and calculating
the mean from this information
C. sending an e-mail to all students asking them to respond with their age and calculating the
mean from those who respond
D. Choices A and C
E. Choices A, B, and C
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13) You read a report that 60% of high-school graduates participated in sports during their
high-school years. You believe that the percentage of high-school graduates who played
sports is higher than what was reported. What type of statistical technique do you use to
see whether you’re right?
A. a confidence interval
B. a z-score
C. a statistic
D. a parameter
E. a hypothesis test
14) You read a report that 60% of high-school graduates participated in sports during their
high-school years. You believe that the percentage of high-school graduates who played
sports in high school is higher than what’s in the report. If you do a hypothesis test to
challenge the report, which of these p-values would you be happiest to get?
A. p = 1
B. p = 0.05
C. p = 0.50
D. p = 0.95
E. p = 0.001
15) The Central Limit Theorem states that, if a random sample of size n is drawn from a
population, then the sampling distribution of the sample mean :
A. is approximately normal if n < 30.
B. is approximately normal if the underlying population is normal.
C. is approximately normal if n ≥ 30.
D. follows a hypergeometric distribution.
E. None of these choices.
16) You’re interested in the willingness of adult drivers (age 18 and over) in a metropolitan
area to pay a toll to travel on less-congested roads. You draw a sample of 100 adult
drivers and administer a survey on this topic to them. Suppose that you collect your data
in a way that makes it likely that the survey respondents aren’t representative of the
target population. What is this called?
A. bias
B. differencing
C. random error
D. sample adjustment
E. transformation
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17) You want to survey students at a high school and calculate the mean age. Which of the
following procedures will result in a simple random sample?
A. selecting one student at random, asking him or her to suggest three friends to participate
and continuing in this fashion until you have your sample size
B. using an alphabetized student roster and selecting every 15th name, starting with the first
one
C. numbering the students by using the school’s official roster and selecting the sample by
using a random number generator
D. classifying the students as male or female and drawing a random sample from each
E. selecting three tables at random from the cafeteria during lunch hour and asking the
students at those tables for their age
18) The p-value in hypothesis testing represents which of the following: (Please select the
best answer of those provided below.)
A. The probability of failing to reject the null hypothesis, given the observed results
B. The probability that the null hypothesis is true, given the observed results
C. The probability that the observed results are statistically significant, given that the null
hypothesis is true
D. The probability of observing results as extreme or more extreme than currently observed,
given that the null hypothesis is true
E. The probability of committing a type II error.
19) A sociologist focusing on popular culture and media believes that the average number of
hours per week (hrs/week) spent using social media is greater for women than for men.
Examining two independent simple random samples of 100 individuals each, the
researcher calculates sample standard deviations of 2.3 hrs/week and 2.5 hrs/week for
women and men respectively. If the average number of hrs/week spent using social
media for the sample of women is 1 hour greater than that for the sample of men, what
conclusion can be made from a hypothesis test where:
𝐻0: 𝜇𝑊−𝜇𝑀=0 and 𝐻a: 𝜇𝑊−𝜇𝑀>0. Use a significance level of 5% .
A. The observed difference in average number of hrs/week spent using social media is not
significant
B. The observed difference in average number of hrs/week spent using social media is
significant
C. A conclusion is not possible without knowing the average number of hrs/week spent using
social media in each sample
D. A conclusion is not possible without knowing the population sizes
E. None of the answers is correct.
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The Table below shows data from a random sample to investigate whether there is a link
between epilepsy and depression.
20) A researcher believes that the proportion of individuals with diagnosed epilepsy that
present with a depressive disorder, pE, is higher than the proportion of individuals
without diagnosed epilepsy that present with a depressive disorder, pNE. Using the data
from the table above and a 0.10 significance level, which of the following is the most
appropriate conclusion given the results?
A. Reject the null hypothesis; there is sufficient evidence to support the researcher’s claim.
B. Fail to reject the null hypothesis; there is sufficient evidence to support the researcher’s
claim.
C. Accept the null hypothesis; there is not sufficient evidence to support the researcher’s
claim.
D. Accept the null hypothesis; there is sufficient evidence to support the researcher’s claim.
E. All answers are incorrect.
21) What does it mean if a test statistic has a p-value of 0.01?
A. There is a 99% chance of getting a value at least that extreme, if the null hypothesis is
false.
B. There is a 1% chance of getting a value at least that extreme, if the null hypothesis is
false.
C. There is a 1% chance of getting that value, if the null hypothesis is false.
D. There is a 1% chance of getting that value, if the null hypothesis is true.
E. There is a 1% chance of getting a value at least that extreme, if the null hypothesis is true.
22) A test was done with a significance level of 0.05, and the p-value was 0.001. Select the
best description of this result.
A. not statistically significant
B. impossible to say without further information
C. highly statistically significant
D. marginally statistically significant
E. statistically significant
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23) One problem with hypothesis testing is that a real effect may not be detected. This
problem is most likely to occur when
A. the effect is small and the sample size is small.
B. the effect is large and the sample size is small.
C. the effect is small and the sample size is large.
D. the effect is large and the sample size is large.
E. The sample is a stratified random sample.
24) A recruiting firm reported that 78% of U.S. companies use social networks such as
Facebook and LinkedIn to recruit job candidates. An economist thinks that the
percentage is higher at technology companies. She samples 70 technology companies
and finds that 55 of them use social networks. The p-value of the hypothesis test to test
her claim at 0.05 level of significance is (round only at the last stage of your calculations)
approximately
A. 0.04
B. 0.45
C. 0.78
D. 0.12
E. 0.98
25) Which type of bias occurs because we do not obtain complete information about a
population?
A. Nonresponse bias
B. No bias
C. Response bias
D. Sampling bias
E. None of the above
26) What would be a type I error?
A. The researcher concludes she has sufficient evidence that her new medication helps
more than insulin injection, and her medication really is better than insulin injection.
B. The researcher concludes she has sufficient evidence that her new medication helps
more than insulin injection, when in reality her medication is not better than insulin
injection.
C. The researcher concludes she does not have sufficient evidence that her new medication
helps more than insulin injection, and her medication really is not better than insulin
injection.
D. The researcher concludes she does not have sufficient evidence that her new medication
helps more than insulin injection, when in reality her medication is better than insulin
injection.
E. The researcher concludes she has sufficient evidence that her new medication controls
blood sugar level the same as insulin injection, and in reality there is a difference.
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27) What would be a type II error?
A. The researcher concludes she has sufficient evidence that her new medication helps
more than insulin injection, and her medication really is better than insulin injection.
B. The researcher concludes she has sufficient evidence that her new medication helps
more than insulin injection, when in reality her medication is not better than insulin
injection.
C. The researcher concludes she does not have sufficient evidence that her new medication
helps more than insulin injection, and her medication really is not better than insulin
injection.
D. The researcher concludes she does not have sufficient evidence that her new medication
helps more than insulin injection, when in reality her medication is better than insulin
injection.
E. The researcher concludes she has sufficient evidence that her new medication controls
blood sugar level the same as insulin injection, and in reality there is a difference.
28) A financial analyst determines the yearly research and development investments for 50
blue chip companies. She notes that the distribution is distinctly not bell-shaped. If the
50 dollar amounts are converted to z-scores, what can be said about the standard
deviation of the 50 z-scores?
A. It depends on the distribution of the raw scores.
B. It is less than the standard deviation of the raw scores.
C. It is greater than the standard deviation of the raw scores.
D. It is equal to the standard deviation of the raw scores.
E. It equals 1.
29) A company has 466 loyal customers and about 1000 customers in total. Your boss asks
you to calculate h hypothesis test whether the proportion of loyal customers is equal to
50%. You tell him that this is inappropriate. Why?
A. The sample size is below 30.
B. The population distribution is not normal.
C. The population proportion is known, so a hypothesis test is not necessary.
D. The sample is biased.
E. The sample size is larger than 10% of the population.
30) A scientist is testing whether a new fertilizer increases the height of a particular plant. As
part of the experiment, 15 of the plants are randomly assigned the new fertilizer, and 15
are randomly assigned an old formula. What type of test should be used to determine
whether the average height of the plants is higher using the new fertilizer?
A. A matched-pairs t-test
B. A one-sample proportion z-test
C. A two-sample proportion z-test
D. A two-sample t-test
E. A chi-squared test of association
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Solutions
Question
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Answer
B
E
B
B
A
C
B
E
A
D
C
A
E
E
C
A
C
D
B
A
E
C
A
B
D
B
D
E
C
D
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Statistical Formulas
Testing one population mean
𝑥̅ − 𝜇0
𝑡= 𝑠
, 𝑑𝑓 = 𝑛 − 1
⁄ 𝑛
√
Testing one population proportion
𝑧=
𝑝̂ − 𝑝0
√𝑝0 (1 − 𝑝0 )
𝑛
𝑛𝑝0 ≥ 5 𝑎𝑛𝑑 𝑛(1 − 𝑝0 ) ≥ 5
Comparing two population means (independent samples)
(𝑥̅1 − 𝑥̅2 ) − 0
𝑡=
2
√𝑠1
𝑛1
+
, 𝑑𝑓 = 𝑚𝑖𝑛{𝑛1 − 1, 𝑛2 − 1}
𝑠22
𝑛2
The paired t-test (dependent samples)
𝑑̅ −0
𝑡 = 𝑠𝑑
⁄√𝑛
𝑑
, 𝑑𝑓 = 𝑛 − 1
Comparing two population proportions (independent samples)
𝑧=
𝑝̂ =
(𝑝̂1 − 𝑝̂2 ) − 0
1
1
√𝑝̂ (1 − 𝑝̂ ) ( + )
𝑛1 𝑛2
𝑥1 +𝑥2
𝑛1 +𝑛2
𝑛1 𝑝̂ ≥ 5, 𝑛1 (1 − 𝑝̂ ) ≥ 5, 𝑛2 𝑝̂ ≥ 5, 𝑛2 (1 − 𝑝̂ ) ≥ 5
Confidence intervals and critical values for the z-distribution
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11
12
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