HYPOTHESIS TESTING
PRACTICE QUESTION
1. Increasing the confidence level from 90% to 95%
would reduce which of the following?
a. The probability of committing a Type I error.
b. The probability of committing a Type II error.
c. The probability of committing a Type I and
Type II error.
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2. Which of the following is a nonparametric
test?
a. A hypothesis test regarding standard
deviation
b. The test of a lognormal distribution
c. A test of randomness.
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3.A pension plan sponsor is evaluating two potential
new managers, Fly by Night (FbN) and Go Get EM
(GGE). The sponsor is considering hiring one of
the firms as an aggressive growth high-risk
manager. He has his junior associate compile the
following statistical data. Based only on these data,
determine whether.
1. The portfolio returns of the two managers are
significantly different
2. The level of risk of the managers is significantly
different.
All decision and relevant data are based on a 5%
level of significance.
FbN
GGE
Average
21%
18%
Standard Deviation of 15%
5%
Past Returns
Acceptance Range :
tmax
2.23
tmin
2.23
Fmin
0
Fmax
2.98
3
tcale for the null hypothesis that the return
difference of the 2 firms is 0 +0.89
Fcale for the null hypothesis that the difference in
of the 2 firms is 0 = 9.0
H 0 : uFbN
H0 :
FbN
uGGF
0
GGF
0
a. Cannot be rejected
rejected
b.Cannot be rejected
c. is rejected
rejected
Cannot be
is rejected
Cannot be
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4.To test the hypothesis of a normal population
mean with unknown variance, one would need
which of the following test statistics when using a
small sample size.
a. Chi-square
b.Normal or z-distribution
c. t-distribution
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5.The marketing director of Aggressive Growth, Ltd.
asserts that the portfolios managed by her firm
produce positive alphas of 8% or more per year,
on average. An analyst suspects that the actual
average alpha is less than 8%. He has collected the
following information.
Sample Size
101
Sample Average :
+6.8%
Sample Standard Deviation :
10%
t-critical @ 10% significance
-1.29
Based on this information, formulate the null
hypothesis to test your suspicion and state the
appropriate conclusion at the 90% confidence
level.
a. The null hypothesis is
hypothesis
b.The null hypothesis is
hypothesis
c. The null hypothesis is
the null hypothesis
6
0
0
0
8% and reject the null
8% and reject the null
8% and cannot reject
6. The null and alternative hypothesis for a one
sided test is :
a. H 0 :
x
b. H 0 :
x
c. H 0 :
x
and H a :
0
0
x
and H a :
and H a :
0
x
x
7
0
0
7.As the level of significance of a hypothesis test
increases :
a. tcritical increases.
b. tcritical decreases
c. tcale increases
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8.Using a 5% level of significance, rejecting the null
hypothesis when it is true is an example of a :
a. Type I error,
b.Type II error,
c. Sampling bias
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9.A hypothesis concerning the variance of the
normally distributed population is tested by using
the :
a. t-statistic
b.z-statistic
c. Chi-square statistic
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10. An analyst claims that the average stock listed
on the London Stock Exchange (LSE) experience
an 8% return. Return of LSE-listed stocks are
normally distributed, and the known population
standard deviation of exchange-listed stock
returns is 5%. An investor in derivative against
an ISE composite portfolio hears this claim, and
worries because 8% represent his breakeven
point (i.e. returns greater than 8% will ruin his
strategy). The investor decides to test the
analyst's claim, but realizes that it is not sufficient
enough to just test if the average return equals
8% - he must verify that the average return is at
most 8%. To this end, the investor takes a sample
of 50 companies listed on the exchange and
calculates a sample mean of 11%. What is the
calculated value of the test statistic and is the
mean return of the exchange-listed stocks less
than or equal to 8% at the 5% level of
significance?
a. 4.24; the population mean is less than or equal
to 8%
b.4.24; the population mean is greater than 8%
c. 0.60; the population mean is less than or equal
to 8%
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11. Ace portfolio management claims that its
growth fund has returned an average of 20% or
better each year since inception. A sample of 5
years of returns has an average annual return of
14.00%, and a standard deviation of 6.708%.
Distribution
t-table
t-table
Chi-sq table
Chi-sq table
Chi-sq table
Df 0.025 0.050 0.100
3 3.182
2.253 1.638
4 2.776
2.132 1.533
3 9.348
7.815 6.251
4 11.143
9.488 7.779
5 12.832 11.070 9.236
Jack Perry, a pension funds consultant suspects
that the actual average return is less than 20%
and wants to test Ace's claim. What is the
appropriate test and what null hypothesis he
should use?
a. t-test H 0: 0 20%
b.t-test. H 0 : 0 20%
c. Chi-sq test H 0 : 0 20%
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