One principle of a justice system is that the defendant in a trial should be
considered innocent until proven guilty.
The null hypothesis would be H0 : The defendant is innocent.
The null hypothesis would be H0 : The defendant is guilty.
The burden of proof lies with the defendant.
The burden of proof lies with the prosecutor.
(Cont’d)
A Type I error would occur if a guilty person is set free.
A Type II error would occur if a guilty person is set free.
"Setting a guilty person free" is considered a less serious mistake than
"falsely convicting an innocent person."
Once you have made a decision, the chance of committing a Type I error is
0 or 1.
Which ones of the following statements are correct?
The probability of committing a Type I error is called the level of
significance.
Type I error is the error of rejecting H0 when it is true.
Type II error is the error of rejecting H0 when it is true.
We would reject the null hypothesis if the significance level is less than the
critical value.
Which ones of the following statements are correct?
A small p-value indicates that the observed data are unlikely if the null
hypothesis is true.
The p-value is the probability of obtaining an observed data that is as
extreme as, or more extreme than, the current, observed data, under the
alternative hypothesis.
We would reject the null hypothesis if the critical value is smaller than the
p-value.
A smaller p-value shows stronger evidence by the data against the null
hypothesis.
Suppose that the significance level for a statistical test is specified at 0.05 and
the obtained p-value is 0.1.
The result is statistically significant.
The result is not statistically significant
A statistically significant result may not be practically significant
We would not reject the null hypothesis,
Which ones of the following statements are correct?
A sample is the whole population.
A parameter is a numerical value that would be calculated based on the
whole population.
A statistic is a numerical value that is calculated based on the sample.
None of the above
0.2 and 0.4 respectively.
0.1 and 0.4 respectively.
0.05 and 0.2 respectively.
0None of the above
(Cont'd)
The events A and B are independent.
The events Ae and B are independent.
Let A1 and A2 be two events. If A1 and A2 are independent, then A1e
and A2 are independent.
If A1 and A2 are mutually exclusive, then A1 and A2 are independent
None of the above.
normal with mean and variances
π and π (1−π ) , respectively.
None of the above
A study was conducted to estimate p, the proportion of college students who
are vegetarians. Based on the results of a random sample of size 225, the 95%
confidence interval for p was found to be (0.20, 0.32). Which ones of the
following statements are true ?
About 95% of college students have between a 20% and a 32% chance of
being vegetarians.
There is a 95% probability that the population proportion lies between 0.20
and 0.32.
The "95% confidence" means that – in repeated experiments, about 95% of
the times the interval (0, 20, 0.32) will cover the sample proportion.
If the sample size increases to 400, we expect the 95% confidence interval
to be wider than the interval (0.20, 0.32).
None of the above.
A random sample of voters from Taiwan is to be selected and asked which ones
of the three president candidates he or she may support. If the margin of error
for the estimated proportion is specified to be 0.03 at 95% confidence, what is
the approximately required sample size?
750
1070
2050
4268
None of the above
Suppose that among a random sample of 2000 voters 1100 plan to vote for the
incumbent president. Develop a 95% confidence interval for the population
proportion that supports the incumbent president.
(0.47, 0-63)
(0.50, 0.60)
(0.51, 0.59)
(0.53, 0.57)
None of the above
Which ones of the following statements are correct?
An index number is a number that expresses the absolute change in price,
quantity, or value compared to a base period
Both the Laspeyres index and the Paasche index are weighted indexes
The moving average is useful in smoothing a time series to see its trend. It
is accomplished by moving the arithmetic mean values through the time
series.
None of the above
size of the dealer
total number of dealers in the country
average age of full-time salespeople employed in the dealer
location of the dealer
none of the above
The sum of residuals are always zero.
There is no other line through the data where the sum of the squared
deviations is smaller.
The i.i.d assumption is necessary for conducting least squares estimation.
Which ones of the following statements are correct?
Multicollinearity exists when dependent and independent variables are
correlated.
We can check for multicollinearity by histogram of the residuals.
If successive observations of dependent variables are correlated, we say that
the data are autocorrelated.
We can check for autocorrelation by the residual plot.
Which ones of the following statements are correct?
In regression, a dummy variable is a variable in which there are only two
possible outcomes. For analysis, we can code one of the outcomes as a 1
and the other a 0.
If a qualitative variable used in a regression model has three possible
outcomes, we can code it by a dummy variable with values −1 , 0, 1.
If a qualitative variable used in a regression model has three possible
outcomes, we can code it by a dummy variable with values 0, 1, 2.
None of the above.
Suppose that the life expectancy of traditional light bulbs follows N(400,σ 2 ),
where σ is the unknown standard deviation. A light bulb company claimed to
have developed a new type of bulbs that can last longer. To conduct the test, 50
new bulbs were randomly selected. The average life expectancy is found to be
406 hours and the sample standard deviation is 20 hours. Set α = 0.05 . The
null and alternative hypotheses are
(Cont'd) The z statistic is
1.65
1.96
2.12
2.65
None of the above
(Cont'd) The critical value is
1.65
1.96
2.12
2.65
None of the above.
(Cont'd) The p-value is:
p − value < 0.025
p − value = 0.025
0.025 < p − value < 0.05
p − value = 0.05
None of the above.
(Cont'd) The probability of committing the Type I error is
0.017
0.025
0.05
0.1
None of the above.
(Cont'd) Approximately what sample size would be necessary in order to have a
95% confidence interval for the population mean with a margin of error of 5 ?
44
62
72
246
None of the above.
(Cont'd) What is the type II error β when the true population mean is 420?
0.0
0.025
0.05
0.1
None of the above.
(Cont'd) A 90% confidence interval for the mean life expectancy of the new
bulbs is
(396,416)
(398,414)
(401,411)
(404,408)
None of the above
A stockbroker reported that the mean rate of return on a sample of 10 oil stocks
was 12.6 percent with a standard deviation of 3.9 percent. The mean rate of
return on a sample of 8 utility stocks was 10.9 percent with a standard
deviation of 3.5 percent. What test statistic can we use to test whither there is
more variation in the oil stocks?
Z
t
F
x2
(Cont’d) The observed test statistic is
3.9/ 3.5
(3.9/ 3.5)2
. 10 / 6 .
None of the above.
Determine the regression equation.
From the ANOVA table, obtain Mean Square to the regression model, Mean
Square due to error, and the F-value.
Write down the H0 and H1 associated with T value = 5.15.
Write down the H0 and H1 associated with F value on the ANOVA
table.
What is the proportion of variation in TSE that can be explained by the
telecom company?
Which range do you expect the middle 95% of the residuals to lie in?
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