The sample median is an unbiased and consistent estimator for the
population mean in random samples.
The variance of the sum of N variables could be larger than the sum of
individual variance of N variables.
If the correlation between two variables is zero, then we are sure that
these two variables are independent.
An analyst computed a chi-square test and concluded he should reject the
null hypothesis at significance level of 5%. Consequently, we know that the
p-value of this chi-square test should be larger than 5%.
The sum of random variables which are independently identically
distributed is normally distributed as the sample size becomes large.
In a supermarket, there are five cashiers awaiting customers. Given five
minutes, there is a 10% chance that one cashier completes service of one
customer and these services are independent. Therefore, the probability
that at least one cashier completes service of one customer is 50%.
The inferential statistics, not descriptive statistics, make use of sample
data to predict population and are for the decision-making purpose.
The nonparametric tests are distribution free but suffer the data
dependency problem.
A financial manager held a portfolio with a market value of $100,000 in
2002. At the end of next four years, the market values of this portfolio were
$105,000, $102,900, $105,987, and $107,046.87, respectively. Therefore,
the geometric and arithmetic mean returns of this portfolio were:
Geometric Mean Arithmetic Mean
1.51% 1.62%
1.72% 1.75%
1.70% 1.81%
1.25% 1.62%
The Ministry of Transportation and Communications (MOTC) reports that
over 10-year period the probability is 0.0012 per month that a car will be
involved with an accident. Suppose there are 20,269,604 registered cars
over this month, then the expected number of cars are involved in
accidents is:
24,323.52
24,434.42
23,412.23
24,044.23
Based on information in question 12, what is the standard deviation of car
accidental rate?
24,295.24
24,296.45
24,294.34
24,290.12
The probability that the stock price of Company A rises 5% is 15% and the
probability that the stock price of Company B rises 5% is 25%. Hence, the
probability that the stock price of at least one company will rise 5% is:
3.75%
36.25%
40%
10%
The probability of neutral stock market performance is:
0.28
0.25
0.90
0.10
The probability for simultaneous good
economy and rising stock performance is:
0.60
0.49
0.27
0.45
An investor has the following
additional information about his portfolio:
1.833%
2.300%
2.365%
2.665%
The expected sample mean and sample variance of bulb duration are 36.5
months and 25 months. What is the coefficient of variation for bulb
duration?
1.46
7.30
0.14
0.68
The expected sample mean and sample variance of bulb duration are 36.5
months and 25 months.
A quality control inspector would like
to know whether the bulb duration is greater than 36 months or not and
calculated t-statistic of bulb duration to be 2.1. What is the sample size?
20
22
441
442
The expected sample mean and sample variance of bulb duration are 36.5
months and 25 months.
Is the bulb duration significantly
greater than 36 months at significance level of 2.5%? (The critical values of
normal distribution at significance levels of 2.5% and 5% equal 1.96 and
1.645, respectively, for the right tail)
Significantly.
Insignificantly.
Undetermined.
Insufficient information to determine.
Two random variables x and y, x has mean 130.45, variance 121.33, and
the sample size of 25 while y has mean 135.01, variance 160.35, and the
sample size of 16. If we want to test if x and y have the same means using t
test, then what are the values of t-statistic and the degree of freedom
assuming equal variance between x and y?
t-statistic Degree of freedom
1.1562 41
1.2234 41
−1.1823 39
−1.2198 39
Based on information in question 21, assuming unequal variance, then
what are the values of t-statistic and the degree of freedom assuming
unequal variance between x and y?
−1.2198 29
−1.1823 29
1.1562 31
1.2234 31
Based on information in question 21, if the correlation between x and y is
−0.35, what is the variance of the sum of x and y?
184.0542
184.0245
184.0425
184.0254
An analyst has the following table for weekly Taiwan Stock Exchange
(TSE) weighted index returns:
0.00400 < u < 0.02400
0.00208 < u < 0.02592
-0.00166 < u < 0.02966
−0.00214 < u < 0.02582
Based on information in question 24, test the null hypothesis that the
mean return is zero. (The critical values of normal distribution at
significance levels of 2.5% and 5% equal 1.96 and 1.645, respectively, for
the right tail)
Insignificantly different from zero at significance level of 5%.
Insufficient information to determine at significance level of 5%.
Insignificantly different from zero at significance level of 10%.
Significantly different from zero at significance level of 10%.
Below are shown the investment performance results of three pension fund
managers who deal with three identical pension programs for past five
months.
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