Download MSc Finance U0W QUANTITATIVE METHODS Class Examples 5 1

MSc Finance U0W
QUANTITATIVE METHODS
Class Examples 5
1.
Which one of the following statements is false?
A. The null hypothesis is what the researcher wants to reject.
B. The decision rule depends on the alternative hypothesis and the
distribution of the test statistic.
C. A Type I error is the rejection of the null hypothesis when it is actually
true.
D. A Type II error is the rejection of the null hypothesis when it is actually
false.
2.
Suppose you are to test a hypothesis to determine the mean time spent on
investment analysis is different from 3 hours per day at the 5% significance level
using a random sample of 64 portfolio managers, which has a mean of 2.5 hours
and a standard deviation of 1.5 hours. Answer the following questions:
a.
The appropriate null hypothesis for the described test is:
A.
B.
C.
D.
Ho: µ = 3 hours.
Ho: µ ≠ 3 hours.
Ho: µ ≤ 3 hours.
Ho: µ ≥ 3 hours.
b.
This is a :
A.
B.
C.
D.
one-tailed test.
two-tailed test.
chi-square test.
A t-test.
The calculated z-statistic is:
A. -2.13.
B. -2.67.
C. 0.33.
D. 2.67.
d. The critical z-values of the test statistic are:
A. -1.976.
B. +1.96.
c.
C.
D.
e.
The 95% confidence interval for the population mean is:
A.
B.
C.
D.
3.
+/-1.96.
+/-2.58.
1.00 < µ < 3.50.
0.54 < µ < 4.46.
2.13 < µ < 2.87.
-1.96 < µ < 1.96.
Which of the following statements about hypothesis testing involving a t-statistic
is most accurate?
The t-statistic is used if the population variance is unknown and the sample is
large.
B. The p-value is the probability of getting a t-statistic at least as far from the
hypothesized z-value as possible.
C. A z-test is theoretically acceptable in place of a t-test for tests concerning a mean
when sample size is small.
D. The t-statistic can be used when the sample is small and the distribution of the
population is not normal.
A.
2.
Excerpt from the cumulative z-table:
Z
2.3
2.4
2.5
0.00
0.9893
0.9918
0.9938
The minimum percentage of the distribution that lie within plus or minus 2.3 standard
deviations from the mean is closest to:
A.
B.
C.
D.
58.33%
97.86%
98.36%
99.18%
3.
Which of the following is the correct structure test for a two-tailed test of the
population mean?
Ho: µ = µ0 versus Ha: µ ≠ µ0
B. Ho: µ ≠ µ0 versus Ha: µ = µ0
C. Ho: µ ≤ µ0 versus Ha: µ > µ0
D. Ho: µ ≥ µ0 versus Ha: µ < µ0
A.
4.
The appropriate test statistic for a test of the equality of variances for two
normally distributed random variables, based on two independent random
samples., is the:
A.
B.
C.
D.
t-test.
F-test.
Chi-square test.
Z-test.
5.
If you are conducting a hypothesis test with a probability of a Type II error of
60% and a probability of a Type I error of 5%, which of the following statements
is most correct:
The power of the test is 40% and there is a probability that the test statistic will
exceed the critical value(s)..
B. There is a probability that the test statistic will be between the critical values of
this is a two-tailed test.
C. The power of the test is 55%, and the confidence level is 95%.
D. There is a 5% probability that the null hypothesis will be rejected when actually
true, and the probability of rejecting the null hypothesis when it is false is 40%.
A.
Define what you think Parametric tests are and what assumptions they rely on.
Define what you think Nonparametric tests are and what assumptions they rely
on.
8. An equity fund claims to have a standard deviation on its monthly returns of 4%,
an estimate based upon its annual return for the 10 years to 2007. To test this is a
valid claim you take the 2008 and 2009 monthly annual returns and found the
standard deviation was 3.8%. Determine if the more recent standard deviation you
have calculated is statistically different form the firm’s claimed 4%.
9. John owns a one-bedroom flat in an area of South London and is considering how
much he might expect to sell it for in the current market. A local estate agent has
told him that the mean price for flats like his in the area is £145,000 and the
population standard deviation is £24,000. To check this information John obtains
a random sample of 40 such properties for sale and finds the mean price is
£150,000. He wishes to test the hypothesis that the area is greater than $145,000
and decides to conduct a hypothesis test at a 1% level of significance. Determine
the following:
a. the appropriate hypothesis;
b. calculate the test statistic;
c. the test structure should John use;
d. the critical value of the statistic;
6.
7.
e.
10.
at a 1% level of significance, whether John should reject or fail to reject the
null hypothesis.
Suppose you are conducting some research on the returns that firms experience
when merger announcements are made for horizontal and vertical mergers. You
estimate the abnormal returns from two samples of the statistical population, as
follows:
Mean
S.D.
Sample size
Abnormal Returns
Horizontal Mergers
1.00%
1.00%
64
Abnormal Returns
Vertical Mergers
2.5%
2.0%
81
Assuming the samples are independent, the population means are normally distributed,
and the population variances are equal, determine if there is a statistically significant
difference in the announcement period abnormal returns for these two types of mergers.