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1.
a.
b.
c.
d.
Parameters are
numerical characteristics of a sample
numerical characteristics of a population
the averages taken from a sample
numerical characteristics of either a sample or a population
2.
a.
b.
c.
d.
Sampling distribution of is the
probability distribution of the sample mean
probability distribution of the sample proportion
mean of the sample
mean of the population
3.
a.
b.
c.
d.
The probability distribution of all possible values of the sample proportion is the
probability density function of
sampling distribution of
same as , since it considers all possible values of the sample proportion
sampling distribution of
4.
a.
b.
c.
d.
Convenience sampling is an example of
probabilistic sampling
stratified sampling
nonprobabilistic sampling
cluster sampling
5.
a.
b.
c.
d.
Which of the following is an example of nonprobabilistic sampling?
simple random sampling
stratified simple random sampling
cluster sampling
judgment sampling
6.
Stratified random sampling is a method of selecting a sample in which
a.
the sample is first divided into strata, and then random samples are taken from each
stratum
b.
various strata are selected from the sample
c.
the population is first divided into strata, and then random samples are drawn from each
stratum
d.
None of these alternatives is correct.
7. A study was conducted to assess a new surgical procedure designed to reduce the incidence of
post-operative complications. The incidence of complications was found to be 40% in 25 patients
having the new procedure and 60% in 20 patients having the old procedure. This difference was
found to be not statistically significant. It may be concluded that
a.
The new procedure is effective in reducing post-operative complications
b.
The new procedure is ineffective in reducing post-operative complications
c.
The sample is biased
d.
The result is clinically significant
8.
a.
b.
c.
d.
The closer the sample mean is to the population mean,
the larger the sampling error
the smaller the sampling error
the sampling error equals 1
None of these alternatives is correct.
9.
a.
b.
c.
d.
Since the sample size is always smaller than the size of the population, the sample mean
must always be smaller than the population mean
must be larger than the population mean
must be equal to the population mean
can be smaller, larger, or equal to the population mean
10.
a.
b.
c.
d.
As the sample size increases, the
standard deviation of the population decreases
population mean increases
standard error of the mean decreases
standard error of the mean increases
Answer of Multiple Choice Questions
1. (B)
7. (B)
2. (A)
8 (B)
3. (D)
9 (D)
4. (C)
10 (C)
5. (D)
6. (C)
1.
A simple random sample from an infinite population is a sample selected such that
a.
b.
c.
d.
each element is selected independently and from the same population
each element has a 0.5 probability of being selected
each element has a probability of at least 0.5 of being selected
the probability of being selected changes
2.
In point estimation
a.
data from the population is used to estimate the population parameter
b.
c.
d.
data from the sample is used to estimate the population parameter
data from the sample is used to estimate the sample statistic
the mean of the population equals the mean of the sample
3.
If we consider the simple random sampling process as an experiment, the sample mean is
a.
b.
c.
d.
always zero
always smaller than the population mean
a random variable
exactly equal to the population mean
4.
The probability distribution of the sample mean is called the
a.
b.
c.
d.
central probability distribution
sampling distribution of the mean
random variation
standard error
5.
The expected value of the random variable is
a.
b.
c.
d.
the standard error
the sample size
the size of the population
None of these alternatives is correct.
6.
The standard deviation of all possible values is called the
a.
b.
c.
d.
standard error of proportion
standard error of the mean
mean deviation
central variation
7. The serum blood glucose was measured for a group of 20 diabetics, then an injection of
insulin was given and after 2 hours another reading for blood glucose was recorded. To assess
the effect of insulin in reducing the blood glucose level we conduct,
a.
b.
c.
d.
Test of significance between two independent means
The degree of freedom for the right test is 38
The paired t-test should be undertaken with degree of freedom of 38
The paired t-test with a degree of freedom should be carried out
8.
As the sample size becomes larger, the sampling distribution of the sample mean
approaches a
a.
b.
c.
d.
binomial distribution
Poisson distribution
normal distribution
chi-square distribution
9.
Whenever the population has a normal probability distribution, the sampling distribution
of is a normal probability distribution for
a.
b.
c.
d.
only large sample sizes
only small sample sizes
any sample size
only samples of size thirty or greater
10.
The sampling error is the
a.
b.
c.
d.
same as the standard error of the mean
difference between the value of the sample mean and the value of the population mean
error caused by selecting a bad sample
standard deviation multiplied by the sample size
Answer of Multiple Choice Questions
1. (A)
7. (C)
2. (B)
8 (C)
3. (C)
9 (C)
4. (B)
10 (B)
5. (D)
6. (B)
1.
Which of the following is considered to be a more efficient estimator?
a.
b.
c.
d.
sample median
sample mode
sample mean
any measure of central location
2.
A population characteristic, such as a population mean, is called
a.
b.
a statistic
a parameter
c.
d.
a sample
the mean deviation
3.
A property of a point estimator that occurs whenever larger sample sizes tend to provide
point estimates closer to the population parameter is known as
a.
b.
c.
d.
efficiency
unbiased sampling
consistency
relative estimation
4.
A sample statistic, such as a sample mean, is known as
a.
b.
c.
d.
a statistic
a parameter
the mean deviation
the central limit theorem
5.
The standard deviation of a point estimator is called the
a.
b.
c.
d.
standard deviation
standard error
point estimator
variance of estimation
6.
A single numerical value used as an estimate of a population parameter is known as
a.
b.
c.
d.
a parameter
a population parameter
a mean estimator
a point estimate
7.
A theorem that allows us to use the normal probability distribution to approximate the
sampling distribution of sample means and sample proportions whenever the sample size is large
is known as the
a.
b.
c.
d.
approximation theorem
normal probability theorem
central limit theorem
central normality theorem
8.
A property of a point estimator that occurs whenever the expected value of the point
estimator is equal to the population parameter it estimates is known as
a.
b.
c.
d.
consistency
the expected value
the estimator
unbiasedness
9.
A simple random sample of size n from an infinite population of size N is to be selected.
Each possible sample should have
a.
b.
c.
d.
the same probability of being selected
a probability of 1/n of being selected
a probability of 1/N of being selected
a probability of N/n of being selected
10.
For a population with any distribution, the form of the sampling distribution of the
sample mean is
a.
b.
c.
d.
sometimes normal for all sample sizes
sometimes normal for large sample sizes
always normal for all sample sizes
always normal for large sample sizes
Answer of Multiple Choice Questions
1. (c)
7. (c)
2. (b)
8 (d)
3. (c)
9 (a)
4. (a)
10 (d)
5. (b)
6. (d)
1.
The absolute value of the difference between the point estimate and the population
parameter it estimates is the
a.
b.
c.
d.
e.
standard error
sampling error
precision
error of confidence
None of the above answers is correct.
2.
The confidence associated with an interval estimate is called the
a.
significance
b.
c.
d.
degree of association
confidence level
precision
3.
A probability statement about the sampling error is known as the
a.
b.
c.
d.
confidence
precision
interval
error
4. In a study about hemoglobin level in pregnant and non-pregnant women, the mean levels in
the two groups were 12 gm/100ml and 14gm/100ml respectively. A test of significance between
the means of the two groups was carried out and the difference was found significant at p<0.05,
this means that the difference
a.
b.
c.
d.
May be attributed to chance
Could be random
Is true and is unlikely to be by chance
Cannot be tested due to insufficient data
5.
As the number of degrees of freedom for a t distribution increases, the difference between
the t distribution and the standard normal distribution
a.
b.
c.
d.
becomes larger
becomes smaller
stays the same
None of the above answers is correct.
6. A clinical trial was designed to test the efficiency of a medicine to reduce the systolic blood
pressure. A group of 20 hypertensive patients were randomly selected and their blood pressure
was recorded. The medicine was administered and a second reading was recorded from the same
group of patients. The convenient test of significance to be conducted is:
a.
b.
c.
d.
One proportion Z-test
Paired t-test
Independent t-test for two means
Two proportion z-test
7. The mean difference at 0.01 (significant level ) is:
a.
b.
c.
d.
Statistically significant difference
Not statistically significant difference
Attributed by chance
Equal
8.
An estimate of a population parameter that provides an interval of values believed to
contain the value of the parameter is known as the
a.
b.
c.
d.
confidence level
interval estimate
parameter value
population estimate
9.
The difference between the point estimate, such as the sample mean, and the value of the
population parameter it estimates, such as the population mean, is known as the
a.
b.
c.
d.
confidence level
sampling error
parameter estimate
interval estimate
10. The mean difference at 0.05 (significant level ) is:
a.
b.
c.
d.
Statistically significant difference
Not statistically significant difference
Attributed by chance
Equal
Answer of Multiple Choice Questions
1. (b)
7. (b)
2. (c)
8 (b)
3. (b)
9 (b)
4. (c)
10 (a)
5. (b)
6. (b)
1.
Whenever the population standard deviation is unknown and the population has a normal
or near-normal distribution, which distribution is used in developing an interval estimation?
a.
b.
c.
d.
standard distribution
z distribution
beta distribution
t distribution
2.
The relationship between α and β is
a.
b.
c.
d.
Direct
Indirect
No relation
all of these
3.
The only way to reduce β and α simultaneously is to
a.
b.
c.
d.
Increase sample size
Increase variance
Increase P-value
all of these
4.
The relationship between the power and α is
a.
b.
c.
d.
Direct
Indirect
No relation
none of these
5.
The power increases as sample size
a.
b.
c.
d.
Increasing
Decreasing
Constant
all of these
6.
In developing an interval estimate, if the population standard deviation is unknown
a.
b.
c.
d.
it is impossible to develop an interval estimate
the standard deviation is arrived at using historical data
the sample standard deviation can be used
None of the above answers is correct.
7.
In order to use the normal distribution for interval esti
population
a.
b.
c.
d.
must be very large
must have a normal distribution
can have any distribution
None of the above answers is correct.
8.
From a population which is not normally distributed and whose standard deviation is not
a.
b.
c.
d.
The normal distribution can be used.
The t distribution with 19 degrees of freedom must be used.
The t distribution with 20 degrees of freedom must be used.
The sample size must be increased.
9.
A sample of 100 elements from a population is selected, and the standard deviation of the
a.
b.
c.
d.
normal distribution
t distribution with 100 degrees of freedom
t distribution with 99 degrees of freedom
None of the above answers is correct.
10.
From a population that is normally distributed, a sample of 25 elements is selected and
the standard deviation of the sampl
distribution to use is the
a.
b.
c.
d.
normal distribution
t distribution
t distribution with 26 degrees of freedom
t distribution with 24 degrees of freedom
Answer of Multiple Choice Questions
1. (d)
7. (b)
2. (b)
8 (d)
3. (a)
9 (a)
4. (a)
10 (d)
5. (a)
6. (c)
1. If the P-value = 0.25, this means that
a.
b.
c.
evidence supports the null hypothesis
There is evidence to reject the null hypothesis
There is a strong evidence to reject the null hypothesis
d.
There is a very strong evidence to reject the null hypothesis
2. The mean height of boys with sickle anemia is
a.
b.
c.
d.
Statistically significant different from the 86.5
Not statistically significant different from the 86.5
Attributed by chance
Equal to 86.5
3.
As the sample size increases, the sampling error
a.
b.
c.
d.
increases
decreases
stays the same
None of the above answers is correct.
4.
For which of the following values of P is the value of P(1 - P) maximized?
a.
b.
c.
d.
P = 0.99
P = 0.90
P = 0.01
P = 0.50
5.
A 95% confidence interval for a population mean is determined to be 100 to 120. If the
a.
b.
c.
d.
e.
becomes narrower
becomes wider
does not change
becomes 0.1
None of the above answers is correct.
6.
0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion
a.
b.
c.
d.
e.
becomes narrower
becomes wider
does not change
Not enough information is provided to answer this question.
None of the above answers is correct.
7.
The ability of an interval estimate to contain the value of the population parameter is
described by the
a.
b.
c.
d.
confidence level
degrees of freedom
precise value of the population mean
None of the above answers is correct.
8.
After computing a confidence interval, the user believes the results are meaningless
because the width of the interval is too large. Which one of the following is the best
recommendation?
a.
b.
c.
d.
Increase the level of confidence for the interval.
Discard the current data and try a different sample.
Increase the sample size.
Reduce the population variance.
9.
If we change a 95% confidence interval estimate to a 99% confidence interval estimate,
we can expect
a.
b.
c.
d.
the size of the confidence interval to increase
the size of the confidence interval to decrease
the size of the confidence interval to remain the same
the sample size to increase
10.
In general, higher confidence levels provide
a.
b.
c.
d.
wider confidence intervals
narrower confidence intervals
a smaller standard error
unbiased estimates
Answer of Multiple Choice Questions
1. (a)
7. (a)
2. (a)
8 (c)
3. (b)
9 (a)
4. (d)
10 (a)
5. (a)
6. (b)
1. As a solution to his criticisms of null hypothesis testing, Loftus (1991;1996) suggested that
researchers should make it their practice to report confidence intervals alongside their statistical
tests.
A. True
B. False
2. The null hypothesis is:
A. the assumption that a significant result is unlikely.
B. the assumption there is no relationship or difference between the variables you are
testing.
C. the assumption that there is a relationship or difference between the variables you are
testing.
D. the pattern between the variables you are testing.
3. Even if there is no real relationship between variables in the population, it is highly likely that
you will find a relationship between variables in your randomly selected sample.
A. True
B. False
4. How can p<.05 be interpreted?
A. There is a 5% chance of you making a type one error.
B. There is a less than 1 in 20 probability of the result occurring by chance alone if the null
hypothesis were true.
C. The probability of obtaining the data if the null hypothesis were true is less than 5%.
D. All of the above.
5. Hypothesis: Higher levels of depression are related to higher levels of anxiety.
Considering this research hypothesis, what would the null hypothesis be?
A. Individuals with lower levels of depression will have higher levels of anxiety. Any result
otherwise observed is the product of chance.
B. There is no relationship between depression and anxiety. Any observed relationship is the
result of chance.
C. There will not be a significant difference between those individuals who score high on
depression, in comparison to those individuals who score high on anxiety. Any observed
difference is the result of chance alone.
D. Individuals with higher levels of depression will have lower levels of anxiety. Any
relationships otherwise observed are the result of chance alone.
6. Hypothesis: Individuals who listen to music whilst revising will achieve significantly higher
exam grades than will individuals who do their revision in silence.
Thinking about this research hypothesis, which of the below would be an appropriate null
hypothesis?
A. There will be no difference in exam grade between those individuals who revise whilst
listening to music and those individuals who revise in silence. Any observed differences
are due to chance alone.
B. Individuals who listen to music whilst revising for their exam will achieve significantly
lower exam grades than will individuals who revise in silence.
C. There will be no relationship between examination grade and the amount of music or
silence experienced during revision. Any observed relationship is the product of chance
alone.
D. The more music an individual listens to when they are revising, the higher their exam
grade will be. In addition, the more silence an individual experiences whilst revising, the
lower their exam grade will be.
7. If you decided to make the critical p-value for significance 0.001 as opposed to the
conventional level of 0.05, what would the consequences be?
A.
B.
C.
D.
You would be less likely to make a type one error.
There would be fewer instances when the null could be rejected.
You would be more likely to make a type two error.
All of the above.
8. Loftus (1991; 1996) criticised hypothesis testing. What was his criticism?
A. Loftus' criticism was that the null hypothesis always states that there is no relationship.
The actual chance of ‘no’ relationship at all being found is very unusual even in
biological sciences. To base probability judgments on this hypothesis is misleading.
B. Loftus' criticism was that it is difficult for researchers to test the null hypothesis when
they cannot access exact p values consistently. The results reported are therefore
misleading.
C. Loftus' criticism was that reporting descriptive statistics and confidence intervals is
misleading when testing the null hypothesis.
D. Loftus' criticism was that the null hypothesis always states that there is a relationship.
The actual chance of a relationship at all being found is very unusual even in biological
sciences. To base probability judgments on this hypothesis is misleading.
9. Look at the hypothesis described in question 7. What are the dependent and independent
variables?
A.
B.
C.
D.
The independent variable is exam grade and the dependent variable is revision condition.
The independent variable is revision condition and the dependent variable is exam grade.
The independent variable is silence and the dependent variable is exam grade.
The independent variable is music and the dependent variable is silence.
10. One of the problems we face when conducting research is that when we select samples from
populations, we might not get a sample that accurately reflects that population.
A. True
B. False
Answer of Multiple Choice Questions
1. (A)
7. (D)
2. (B)
8 (A)
3. (B)
9 (B)
4. (D) 5. (B)
10 (A) 11(D)
6. (A)
1. Sometimes, due to _____, we are likely to get patterns of scores in our samples that do not
accurately reflect the underlying population.
A.
B.
C.
D.
sampling error
scattergrams
probability
relationships between variables
2. The p-value is sometimes misinterpreted. It represents the probability of a relationship
occurring by chance if the null hypothesis is true. Therefore it assumes that the null is true.
A. True
B. False
3. The second criticism Loftus (1991; 1996) raised was that psychologists don't give enough
consideration to the _____________ when reporting their results.
A.
B.
C.
D.
exact p value
statistical tests
null hypothesis
population means
4. What does a p-value generally tell us?
A. The p-value tells us the likelihood of our obtaining the pattern of results due to sampling
error if there is not a relationship between our variables in the population.
B. The p-value tells us the likelihood of our obtaining the significant result due to a
relationship between our variables in the population.
C. The p-value tells us the likelihood of our obtaining the pattern of results due to variance if
there is not a relationship between our variables in the population.
D. The p-value tells us the likelihood of our obtaining the pattern of results due to sampling
error if there is a population.
5. What is a type one error?
A.
B.
C.
D.
A type one error is obtaining a non-significant result by sampling error alone.
A type one error is where we reject the null hypothesis when it is true.
A type one error is obtaining a non significant result when it should be significant.
None of the above.
Answer of Multiple Choice Questions
1. (A)
2. (A)
3. (D)
4. (D)
5. (B)