A bag contains 3 white and 4 green balls. What is the probability that if 2 balls are
drawn at random without replacement, both the balls are white?
1/ 4
1/ 5
1/ 6
1/ 7
For a continuous random variable X, the probability of any single value of X is:
one
zero
determined by the cumulative function
determined by the probability density function
The joint probability distribution function of two random variables X and Y is as
f (x, y) = x + 3y , 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 . Then, the random variables in this
question are:
independent
dependent
neither independent nor dependent
cannot answer based on the information provided
A distribution of returns that has a greater percentage of small deviations from the mean
and a greater percentage of extremely large deviations from the mean:
is positively skewed
is a symmetric distribution
has positive excess kurtosis
has negative excess kurtosis.
Which of the following is most accurate regarding a distribution of returns that has a
mean greater than its median?
It is positively skewed
It is a symmetric distribution
It has positive excess kurtosis
It has negative excess skewness.
Which of the following statements about skewness and kurtosis is FALSE?
Kurtosis is measured using deviations raised to the fourth power
Positive values of kurtosis indicate a distribution that has fat tails, referred to as
platykurtic
Values of relative skewness in excess of 0.5 in absolute value indicate large levels
of skewness
Relative skewness is equal to the absolute skewness divided by the cubed standard
deviation.
What is the appropriate test statistic for constructing confidence intervals for the
population mean of a normal distribution when the population variance is unknown?
The Z-statistic at α with n degrees of freedom
The Z-statistic with n-1 degrees of freedom
The t-statistic at α/ 2 with n degrees of freedom
The t-statistic at α/ 2 with n-1 degrees of freedom.
What is the appropriate test statistic for constructing confidence intervals for the
population mean of a abnormal distribution when the population variance is unknown
and the sample size is large?
The Z-statistic or the t-statistic
The Z-statistic at α with n degrees of freedom
The t-statistic at α with 29 degrees of freedom
The t-statistic at α/ 2 with n degrees of freedom.
In a sample of 100 students, 60 indicated that they were opposed to a tuition increase to
fund a new athletic facility. Which of the following is closest to the 90 percent
confidence interval for the population proportion of all students opposed to the tuition
hike?
0.52 to 0.60
0.50 to 0.70
0.52 to 0.68
0.55 to 0.67
The mean lifetime mileage and variance of 50 Brand X tires was 40,000 and 5,000,
respectively. The mean lifetime mileage and variance of 75 Brand Y tires was 48,000
and 6,500, respectively. Which of the following is closest to the 95 percent confidence
interval for the difference in the mean lifetime mileage of Brand Y and Brand X tires?
7,973 to 8,027 miles
7,967 to 8,023 miles
7,634 to 8,366 miles
7,413 to 8,587 miles.
Which of the following statements about hypothesis testing is TRUE?
A Type II error is rejecting the null when it is actually true
If the p-value is greater than the significance level, fail to reject H0
The significance level equals one minus the probability of a Type I error
If the alternative hypothesis H1 :μ > μ0 , then the test is a two-tailed test
Which of the following statements is FALSE?
A Type I error is rejecting the null when it is actually true
Failing to reject the null when it is false is an example of a Type II error
The probability of committing a Type I error is the significance level of the test
If a person is presumed innocent unless proven otherwise, finding a guilty person
innocent is an example of a Type II error.
In a hypothesis test, the null hypothesis is that the population mean is equal to 90 versus
the alternative hypothesis the population mean is not equal to 90. A sample of 100
elements selected from this population produced a mean of 84 and a standard deviation
of 10. If hypothesis testing is conducted at the 5 percent significance level, the
CORRECT decision is to:
reject the null hypothesis
fail to reject the null hypothesis
accept the alternative hypothesis
It is impossible to reach a decision because of the large value for the computed Z.
A study was conducted to determine whether the standard deviation of monthly
maintenance costs of a Pepper III aircraft is $300. A sample of 30 Pepper IIIs had a
monthly maintenance costs of $3,025 and a standard deviation of $325. Using a 5
percent level of significance, which of the following is the most appropriate conclusion
regarding the difference between the hypothesized value of the population variance and
the sample variance?
(*The critical chi-square values are 16.047 on the left and 45.722 on the right.)
The difference is not meaningful
The population and sample variances are significantly different
The population and sample variances are not significantly different
There are no tests that may be used to test variance differences of small samples.
What is the computed value of the test statistic that follows an F-distribution when
sample variances are equal and the level of significance is 0.10?
0.10
0.90
1.00
0.05
Which of the following is not a common characteristic between the F-distribution and
chi-square distribution? They:
are both asymmetrical
are both bound by zero on the left
are both defined by degrees of freedom
both have means that are less than their standard deviations.
Three events, X, Y, and Z are considered independent if they are pairwise independent. That is:
P(X and Y) = P(X)P(Y)
P(Y and Z) =P(Y)P(Z)
P(X and Z) = P(X)P(Z)
P(X and Y and Z) = P(X)P(Y)P(Z)
What are the basic assumption behind regression models?
Stochastic regressors
The independent variables have to be independent
Error terms are uncorrelated
Error terms all have constant variances.
What are the ways to overcome the autocorrlation problem in regression analysis?
Addition of independent variables
Omission of independent variables
Transforming variables
Use of Autoregression
There are some assumption for the F test in ANOVA to be valid and those assumption are
Normality
Large sample sizes
Equal variances
Independence
A manufacturer has purchased a lot of 1700 ring seals from a producer. The
manufacturer's inspectors are using a single-sample acceptance sampling plan to decide
whether or not to accept the lot. The sample size is 10, and if the inspectors find any
seals out of conformance in the sample, the lot will be rejected.
Suppose the lot has 5% nonconforming seals and that this is acceptable to the
manufacturer. The producer's risk is 32%
Suppose the lot has 5% nonconforming seals and that this is acceptable to the
manufacturer. The producer's risk is 40%
Suppose the lot contain 14% nonconforming seals and that this is unacceptable to
the manufacturer. The consumer's risk is 22%
Suppose the lot contain 14% nonconforming seals and that this is unacceptable to
the manufacturer. The consumer's risk is 28%
In a simple linear regression analysis, which of the following are true
The F test and t test may or may not yield the same results
The relationship between X and Y is represented a straight line
The value of F = t 2
Sum of the residuals always is zero
Which of the following statements for multicollinearity in regression analysis are
correct?
It is difficult to interpret the estimates of the regression coefficients
Inordinately small t value for the regression coefficient may result
The standard deviation of regression coefficients are underestimated
The algebraic sign of estimated regression coefficients may be the opposite of what
would be expected for a particular predictor variable
Which of the following statements for Paasche Price Index are correct?
Paasche Price Index is weighted aggregate price index computed by using the
quantities of the based years for all other years
The advantage of this index is that it incorporates current quantities figures in the
calculations
The disadvantage is that ascertaining quantity figures for each time period is
expensive
All of above are correct
Which of the following statements for heteroscedasticity in regression model are
correct?
Heteroscedasticity can arise as a result of the presence of outlier
Heteroscedasticity destroy the unbiasedness and consistency properties of OLS
estimators
OLS estimators are no longer minimum variance or efficient
All of above are correct
Which of the following statements for autocorrelation in regression model are correct?
Autocorrelation can arise because of inertia or sluggishness in economic time-series
Autocorrelation could be resulted from using the incorrect functional form
OLS estimators remain unbiased as well as consistent
OLS estimators remain efficient
Which of the following statements for nonparametric statistics are correct?
Nonparametric statistics are based in fewer assumptions about the population than
parametric statistics
The computations on nonparametric statistics are usually less complicated than
those for parametric statistics, particular for large samples
Probability statements obtained from most nonparametric tests are exact
probabilities
Nonparametric testes can be wasteful of data if parametric tests are available for use
with the data
Which of the following tests is used to determine whether an additional variable makes
a significant contribution to a multiple regression model?
t test
Z test
F test
Chi-square test
When a qualitative variable is entered into a model by using dummy variables,
The number of dummy variables entered for the qualitative variables equals the
number of levels of the qualitative variable
The number of dummy variables entered for the qualitative variables always one
less than the number of levels of the qualitative variable
Only one dummy variable needs to be entered into the model
None of above is correct
A person wishes to compare the means of three populations. The data is ordinal. Which
of the following should be used?
One-way analysis of variance
Kruskal-Wallis
Wilcoxon
Mann-Whitney
Most "Before and After " types of experiments should be analyzed using
Chi-square goodness of fit test
Kruskal-Wallis test
Mann-Whitney U test
Wilcoxon test
Which of the following is an acceptable method to identify multicollinearity in a
regression model?
Examine a residual plot
Examine the ANOVA table
Examine a correlation matrix
Examine the partial regression coefficients
How does the classical methodology choose a regression model in the first place?
Please list the criteria and explain.
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