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Students Offering Support (SOS)
EC255: Managerial Statistics
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Fall 2017 Mock Midterm
https://www.coursehero.com/file/64674267/EC255-Mock-Midterm-2pdf/
1. According to the central limit theorem, for samples of size 95 drawn from a population
with µ = 400 and σ = 26, the mean of the sampling distribution of sample means is __.
a. 15
b. 4
c. 400
d. 26
e. 40
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2. According to the central limit theorem, for samples of size 16 drawn from a population
with µ = 86 and σ = 36, the standard error of the mean of sample means is __.
a. 36
b. 16
c. 9
d. 4
e. 25
3. Suppose a population has a mean of 90 and a standard deviation of 40. If a random
sample of size 64 is drawn from the population, the probability of drawing a sample with
a mean between 80 and 100 is ___.
a. 0.8414
b. 0.4772
c. 0.4207
d. 0.9544
e. 1.0000
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4. Suppose a population has a mean of 45 and a standard deviation of 18. If a random
sample of size 9 is drawn from the population, the probability of drawing a sample with
a mean of more than 60 is ___.
a. 0.4938
b. 0.5000
c. 0.1000
d. 0.0062
e. 0.0062
5. Suppose that 30% of a population possess a given characteristic. If a random sample size
of 200 is drawn, then the probability that 35% or fewer of the samples possess the
characteristic is ___.
a. 0.9382
b. 0.4382
c. 1.0000
d. 0.4207
e. 0.9207
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6. A population proportion is 0.48. Suppose a random sample of 500 items is sampled for
this population. What is the probability that the sample proportion is greater than 0.50?
a. 0.3413
b. 0.1841
c. 0.5000
d. 0.3133
e. 0.1587
7. Jessica, Director of Research, is evaluating consumer acceptance of the new banking
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mobile app. Her research suggests that 37% of a random sample of 100 individuals prefer
the new app to the old one. If Jessica concludes that 37% of all individuals prefer the
new app, she is using a ___.
a. An interval estimates
b. An exact estimate
c. A statistical parameter
d. A range estimate
e. A point estimate
8. The z-value associated with a two-sided 95% confidence interval is ___.
a.
b.
c.
d.
e.
1.28
1.96
1.645
2.33
2.575
9. The table t value associated with the upper 10% of the t distribution and 14 degrees of
freedom is ___.
a. 1.761
b. 1.729
c. 1.345
d. 2.228
e. 2.145
10. A researcher wants to determine the sample size necessary to adequately conduct a
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study to estimate the population mean to within 10 points. The range of population
value is 100 and the researcher plans to use a 95% level of confidence. The sample size
should be at least ___.
a. 25
b. 20
c. 692
d. 700
e. 310
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11. Suppose a random sample of size 36 is selected from a population yielding a sample
mean of 26. The population standard deviation is 16. From this information, the 90%
confidence interval to estimate the population mean can be computed to be ___.
a. 20.97 to 31.03
b. 20.54 to 31.46
c. 21.61 to 30.39
12. A researcher is interested in estimating the mean value for a population. She takes a
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random sample of 21 items and computes a sample mean of 194 and a sample standard
deviation of 45. She decides to construct a 95% confidence interval to estimate the
mean. The degrees of freedom associated with this problem are ___.
a. 18
b. 17
c. 16
d. 15
e. 20
13. Random sample of 200 items from population result in 65% possessing a given
characteristic. The research constructs a 95% confidence interval to estimate the
population proportion. The resulting confidence interval is ___.
a. 0.55 to 0.75
b. 0.58 to 0.72
c. 0.52 to 0.78
d. 0.60 to 0.70
e. 0.68 to 0.78
14. Consider the following null and alternative hypotheses:
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Ho: µ ≤70
Ha: µ >70
These hypotheses ___.
a. Indicate a one-tailed test with a rejection area in the right tail
b. Indicate a one-tailed test with a rejection area in the left tail
c. Indicate a two-tailed test
d. Are not mutually exclusive
e. Are established incorrectly
15. Consider the following null and alternative hypotheses:
Ho: µ=70
Ha: µ≠70
These hypotheses ___.
a. Indicate a one-tailed test with a rejection area in the right tail
b. Indicate a one-tailed test with a rejection area in the left tail
c. Indicate a two-tailed test
d. Are not mutually exclusive
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16. A researcher is testing a hypothesis of a single mean. The critical z value for α = .10 and
a two-tailed test is +1.645. The observed z value from sample data is 1.85. The decision
made by the researcher based on this information is to ___ the null hypothesis.
a. Reject
b. Not Reject
c. Redefine
d. Change Alternate Hypothesis into
e. Restate null hypothesis
17. Suppose you are testing the null hypothesis that a population mean is less than or equal
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to 78, against the alternative hypothesis that the population mean is greater than 78. If
the sample size is 36 and α = .10, the critical value of z is ___.
a. 1.645
b. -1.645
c. 1.28
d. -1.28
e. 2.33
18. Suppose you are testing the null hypothesis that a population mean is greater than or
equal to 55, against the alternative hypothesis that the population mean is less than 55.
The sample size is 64 and α = .05. If the sample mean is 50 and the population standard
deviation is 16, the observed z value is ___.
a. -1
b. 1
c. 2.5
d. -2.5
e. 8
19. In performing a hypothesis test where the null hypothesis is that the population mean is
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7.9 against the alternative hypothesis that the population mean is not equal to 7.9, a
random sample of 25 items is selected. The sample mean is 8.1 and the sample standard
deviation is 3.4. It can be assumed that the population is normally distributed. The
observed "t" value for this problem is ___.
a. 0.29
b. 1.33
c. 1.29
d. 0.05
e. 0.20
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20. In performing a hypothesis test where the null hypothesis is that the population mean is
9.9 against the alternative hypothesis that the population mean is not equal to 9.9, a
random sample of 21 items is selected. The sample mean is 10.2 and the sample
standard deviation is 2.9. It can be assumed that the population is normally distributed.
The level of significance is selected as 0.05. The table "t" value for this problem is ___.
a. 2.528
b. 1.812
c. 1.725
d. 2.131
e. 2.086
21. Consider the following null and alternative hypotheses:
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Ho: p ≥0.21
Ha: p <0.21
These hypotheses ___.
a. Indicate a one-tailed test with a rejection area in the right tail
b. Indicate a one-tailed test with a rejection area in the left tail
c. Indicate a two-tailed test
d. Are not mutually exclusive
e. Are established incorrectly
22. After constructing a confidence interval for the difference between means μ 1 − μ 2 ,
you believe that the interval is not useful because it is too wide. In order to correct this
problem, you need to:
a. Increase the standard deviation of the population
b. Increase the level of confidence
c. Increase the same sizes
d. Increase the same mean of μ 1
23. If critical z increases, the confidence interval will__________, and if alpha increases,
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the confidence interval will____________?
a. Increase; Increase
b. Decrease; Decrease
c. Increase; Decrease
d. Neither of the above
24. Which of the following statements is NOT true in regard to confidence intervals &
hypothesis testing?
a. As confidence level rises, the critical z value also rises
b. As level of significance of a hypothesis increases, the confidence interval value
will fall
c. Interval Estimate (Confidence Interval) are the range of values within which
the analyst can declare, with some confidence, that the population parameter
lies.
d. Alpha represents the region within the confidence interval.
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25. Siddharth, a prestigious financial investor has just got his first job. He wants to impress
his boss with some amazing research, but he knows he will need to use his knowledge
from managerial statistics. He is interested in determining the significant differences
in P/E ratios across two years. Siddarth has sampled 9 organizations listed on the TSX
and recorded the appropriate P/E ratios. Determine the rejection decision. Assume the
sample mean is 5.03, and the sample standard deviation is 21.60. Assume the following
hypothesis statement is two tailed. Determine the statistical conclusion, given that H0
is rejected if t < -tα/2,n – 1 or t > tα/2,n – 1.
Ho: D = 0
Ha: D ≠ 0
n= 9, df= 8
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d  5.03
sd  21.60
Alpha = 0.01
a.
b.
c.
d.
Statistical
Statistical
Statistical
Statistical
t=
t=
t=
t=
0.6986,
0.3400,
0.6986,
0.3400,
Critical
Critical
Critical
Critical
t=
t=
t=
t=
3.355,
3.444,
3.355,
3.444,
reject the null hypothesis
reject the null hypothesis
not reject the null hypothesis
not reject the null hypothesis
Niraj has decided to do investigation into the hourly wages for law & accounting, and
has determined this data below. Using this data, answer question 26, 27, 28, 29.
Accounting
n1 = 30
x1 = 70
𝜎1 = 12
Law
n2 = 45
X2 = 90
𝜎2 = 15
Ho: μ1 = μ2
Ha: μ1 ≠ μ2
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α = 0.05
26. The observed z value is___?
a.
b.
c.
d.
-6.39
6.39
-3.60
3.60
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27. The critical z value is___?
a.
b.
c.
d.
+/- 1.96
+/- 1.645
+ 1.96
-1.645
28. The margin of error is____?
a.
b.
c.
d.
5.60
4.56
6.13
2.35
29. The standard error of difference is____?
3.13
4.56
5.33
-3.13
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a.
b.
c.
d.
30. Jayanth & Ragavi determined the following values. The statistic z is______?
Population One
p̂= 0.5
P-bar = 0.6
n1 = 20
Population Two
p̂= 0.3
q-bar =0.4
n2 = 40
Additional info:
𝐻0 : 𝜇 1 − 𝜇 2 ≤ 0
𝐻𝑎 : 𝜇 1 − 𝜇 2 > 0
a.
b.
c.
d.
1.56
2.44
-1.56
1.49
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You have finished the mock midterm (Answers are on the next page)! YAY!
Now continue studying so you can ace this midterm!
Best of luck on Friday!
Sincerely,
Your SOS EC255 Tutors & Coordinator
https://www.coursehero.com/file/64674267/EC255-Mock-Midterm-2pdf/
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1. C
2. C
3. D
4. D
5. A
6. B
7. E
8. B
9. C
10. A
11. C
12. E
13. B
14. A
15. C
16. A
17. C
18. D
19. A
20. E
21. B
22. C
23. C
24. D
25. C
26. A
27. A
28. C
29. A
30. D
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Solutions
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