Download 1) At a charity ball, 800 names were put into a hat. Four of the names

1) At a charity ball, 800 names were put into a hat. Four of the names are
identical. On a random draw, what is the probability that one of these
four names will be drawn?
A. 0.004.
B. 0.005.
C. 0.010.
D. 0.025.
B. P(E)=4/800=1/200=0.005
2) Which one of these statistics is unaffected by outliers?
A. Mean
B. Interquartile range
C. Standard deviation
D. Range
B. Interquartile range.
3) Which of the following would indicate that a dataset is not bell‐
shaped?
A. The range is equal to 5 standard deviations.
B. The range is larger than the interquartile range.
C. The mean is much smaller than the median.
D. There are no outliers.
Answer: C.
4) The average U.S. dollar/Euro exchange rate from a sample of 36
monthly observations is $1.00/Euro. The population variance is 0.49.
What is the 95% confidence interval for the mean U.S. dollar/Euro
exchange rate?
A. $0.5100 to $1.4900.
B. $0.7713 to $1.2287.
C. $0.8075 to $1.1925.
D. $0.8657 to $1.1343.
Answer: B
The population standard deviation is the square root of the variance
(√0.49 = 0.7).
Because we know the population standard deviation, we use the z‐
statistic.
The z‐statistic reliability factor for a 95% confidence interval is 1.960.
The confidence interval is $1.00 ± 1.960($0.7 / √36) or $1.00 ± $0.2287.
5) The approximate 99% confidence interval for the population mean
based on a sample of 60 returns with a mean of 7% and a sample
standard deviation of 25% is closest to:
A. ‐1.31% to 15.31%.
B. 1.58% to 14.58%.
C. 0.54% to 13.45%.
D. 1.32% to 13.45%.
Answer: A.
If you use a z‐statistic, the confidence interval is
7% ± 2.58(3.227) = ‐1.326% to 15.326%, which is closest to the correct
choice.
6) The mean monthly return for an equity portfolio over 60 months is
1.5%. The standard deviation is 3.0%. The value of the test statistic to
test the hypothesis that mean monthly return is equal to zero is closest
to:
A. 30.00
B. 3.87.
C. 0.50.
D. 2.19.
Answer :B
z = (1.5% - 0.0%) / [(3.0% / √60)] = 3.87
7) Analyst is testing the null hypothesis that the population mean is less
than or equal to 45. A random sample of 81 observations selected from
this population produced a mean of 46.3.
The population has a standard deviation of 4.5.
The value of the appropriate test statistic for the test of the population
mean is:
A. z = –2.75.
B. z = 2.60.
C. t = 3.84.
D. t = 4.60.
Answer: B
The population variance is known and the sample size is large.
The test statistic is:
8) A survey is taken to determine whether the average starting salaries
of CFA charterholders is equal to or greater than $59,000 per year. What
is the test statistic given a sample of 135 newly acquired CFA
charterholders with a mean starting salary of $64,000 and a standard
deviation of $5,500?
A) 0.91.
B) ‐10.56.
C) ‐0.91.
D) 10.56.
Answer: D.
With a large sample size (135) the z‐statistic is used. The z‐statistic is
calculated by subtracting the hypothesized parameter from the
parameter that has been estimated and dividing the difference by the
standard error of the sample statistic. Here, the test statistic = (sample
mean – hypothesized mean) / (population standard deviation / (sample
size)1/2) = (X − µ) / (σ / n1/2) = (64,000 – 59,000) / (5,500 / 1351/2) =
(5,000) / (5,500 / 11.62) = 10.56.
9) Analyst wants to test if the mean price of houses in the area is greater
than $145,000. A random sample of 36 houses in the area has a mean
price of $149,750. The population standard deviation is $24,000, and the
analyst wants to conduct hypothesis testing at a 1 percent level of
significance.
H0: m≤145,000 ; Ha: m>145,000
At a 1 percent level of significance, the analyst should:
A.
fail to reject the null
hypothesis.
B. accept the null hypothesis.
C. reject the null hypothesis.
D. neither reject nor fail to reject the null hypothesis.
Answer: A.
The value of the calculated test statistic is
For a one‐tailed z‐test at the 1% level of significance, the critical z‐value
is z0.01 = 2.33. Since the test is one‐tailed on the upper end (i.e., Ha: µ >
145,000), we use a positive z‐critical value.
The decision rule is: reject H0 if z‐computed > z‐critical. Since 1.1875 <
2.33, the analyst will fail to reject the null.
10) An analyst estimates the stock has a 40% chance of earning 10%, a
40% chance of earning 12.5%, and a 20% chance of earning 30%. What is
the stock’s standard deviation of expected returns?
A. 5%
B. 5.57%
C. 7.58%
D. 9.99%
C. Expected value =0.4*0.1+0.4*0.125+0.2*0.3= 15%
Variance=0.4*(0.10‐0.15)+0.4*(0.125‐0.15)+0.2*(0.30‐0.15)=57.5%,
St.Dev.=sqrt(57.5%)=7.58%
11) A random sample of 40 students has a test score with sample mean
81.5 and sample standard deviation 10.2.
Construct the confidence interval for the population mean, μ if
c = 0.90.
A. (71.8, 93.5)
B. (78.8, 84.2)
C. (66.3, 89.1)
D. (51.8, 92.3)
The correct answer is: B.
=NORMINV(0.05,81.5,10.2/SQRT(40)) = 78.8
=NORMINV(0.95,81.5,10.2/SQRT(40)) = 84.2
12) An analyst is conducting a hypothesis test to determine if the mean
time spent on investment research is different from 3 hours per day. The
test is performed at the 5 percent level of significance and uses a
random sample of 64 portfolio managers, where the mean time spent on
research is found to be 2.5 hours. The population standard deviation is
1.5 hours.
Which of the following decisions is the CORRECT decision for this study?
A.
Fail to reject the null hypothesis.
B.
The sample size is too small, so increase the sample size.
C.
No decision is possible because the sample standard deviation was
not given.
D.
Reject the null hypothesis.
The correct answer is: D.
The calculated z‐statistic is:
At α/2 = 0.025, the critical z‐values are: ±zα/2 = ±z0.025 = ±1.96.
Decision rule:
Reject H0 if zcomputed < –1.96, or zcomputed > +1.96.
Since –2.67 < –1.96 , reject H0.