MSU STT 201 Final Exam – Questions With Solutions
Which of the following helps determine the standard error for a confidence
interval for a mean?
A. The sample size(s)
B. The sample estimate
C. The true value of the population parameter
D. The confidence level Right Ans - A
The distinction between sampling distribution and a confidence interval is:
A. A confidence interval gives possible values for a population parameter
when only a single value of a sample statistic is know
B. A sampling distribution gives possible values for a sample statistic when
the population parameter is assumed to be known, while a confidence interval
gives possible values for a population parameter when only a single value of a
sample statistic is known
C. Sampling distributions exist only for situations involving means, while
confidence intervals can be computed for situations involving means and
proportions
D. Confidence intervals exist only for situations involving means, while
sampling distributions can be computed for situations involving means and
proportions Right Ans - B
(distribution = numerous values ---> single value
C.I. = single value --> fixed values)
Which of the following is NOT true about the standard error of a statistic?
A. The standard error measures, roughly, the average difference between the
statistic and the population parameter
B. The standard error is the estimated standard deviation of the sampling
distribution for the statics
C. The standard error can never be a negative number
D. The standard error increases as the sample size(s) increases Right Ans -
D
(s.e. & sample sz do opposite of one another)
,For a randomly elected sample of n=36 men's height, it is reported that the
standard error of the mean is 0.5 inches. Three of the following statements are
true, while one is false. Which statement is false?
A. The standard error (0.5 inches) is an estimated value of the standard
deviation of the sample mean
B. If a new sample of n= 30 men's height is collected, the standard error of the
mean might not equal 0.5 inches.
C. Over many different samples of n=36 men's heights, the average difference
between the sample means and population mean will be roughly 0.5 inches.
D. In about 95% of all samples of n= 36 men's heights, the same mean will be
within 0.5 inches of the population mean Right Ans - D
What is the primary purpose of a 95% confidence interval for a mean?
A. to estimate a sample mean
B. to test a hypothesis about a sample mean
C. to estimate a population mean
D. to provide an interval that covers 95% of the individual values in the
population Right Ans - C
(C.I. = pop mean)
The confidence level for a confidence interval for a mean is:
A. the probability the procedure provides an interval that covers the sample
mean
B. the probability of making a Type 1 error if the interval is used to test a null
hypothesis about the population mean
C. the probability that individuals in the population have values that fall into
the interval
D. the probability the procedure provides an interval that covers the
population mean Right Ans - D
Which of the following will NOT result in paired data?
A. The same measurement is taken twice on each person, under different
conditions or at different times
,B. Similar individuals are paired before giving the treatments in an
experiment. Each member of a pair then receives a different treatment. the
same response variable is measured for all individuals
C. Two different variables are measured for each individual. There is interest
in the amount of difference between the two variables
D. One random sample is taken, and a variable is recorded for each individual,
but then units are categorized as belonging to one population or another
Right Ans - D
(paired = before and after studies, non-independent)
Which of the following statements is most correct about a confidence interval
for a mean?
A. It provides a range of values, any of which is a good guess at the possible
value of the sample mean
B. It provides a range of values, any of which is a good guess at the possible
value of the population mean
C. It provides a good guess for the range of values the sample mean is likely to
have in repeated samples
D. It provides a good guess for the range of values the population mean is
likely to have in repeated samples Right Ans - B
(C.I. = pop mean)
When constructing a confidence interval for the different in two population
means, it is appropriate to use the pooled standard error only when:
A. the population standard deviations can be assumed to be equal
B. the sample standard deviations are exactly equal
C. the population means can be assumed to be equal
D. the sample means are exactly equal Right Ans - A
(pooled = same pop s.d.)
Which of the following ways of collecting data would result in two
independent samples?
, A. A sample of college students is measured for stress both before and after
taking an important exam
B. A group of college students are paired based on gender, age, and grades.
One student in a pair receives stress management training and the other one
does not. After a few weeks all students are measure for stress right before an
important exam
C. A sample of English majors is measured for stress before taking an
important exam. A sample of engineering majors is also measured for stress
before taking their important exam.
D. A sample of college students is measured for stress before taking an
important exam. Their exam grade is also recorded. Right Ans - C
Random samples of 200 men and 200 women were collected and their resting
pulse rates were measure, to estimate how much mean resting rates differ for
men and women in the population. An analyst mistakenly paired the
observations and constructed an approximate 95% confidence interval for the
mean difference to be
(5 +/- 2 x 0.2) beats per minute. If the data had been analyzed correctly,
finding an approximate 95% confidence interval of the difference in
population means, which of the following parts of the interval would be
different?
A. The sample statics of 5 beats per minute
B. The multiplier of 2
C. The standard error of 0.2
D. None of the parts would be different; it is an equivalent analysis Right
Ans - C
(multiplier is already representative of 95% C.I -->
1+ .95/ 2 --> invT: .975, 99 ~ 2
&
sample statistic is unaffected by C.I.)
A researcher asked random samples of 50 kindergarten teachers and 50 12th
grade teachers how much money they pent out-of-pocket on school supplies
in the previous school year, to see if teachers at one result, it is reasonable to
conclude that:
Which of the following helps determine the standard error for a confidence
interval for a mean?
A. The sample size(s)
B. The sample estimate
C. The true value of the population parameter
D. The confidence level Right Ans - A
The distinction between sampling distribution and a confidence interval is:
A. A confidence interval gives possible values for a population parameter
when only a single value of a sample statistic is know
B. A sampling distribution gives possible values for a sample statistic when
the population parameter is assumed to be known, while a confidence interval
gives possible values for a population parameter when only a single value of a
sample statistic is known
C. Sampling distributions exist only for situations involving means, while
confidence intervals can be computed for situations involving means and
proportions
D. Confidence intervals exist only for situations involving means, while
sampling distributions can be computed for situations involving means and
proportions Right Ans - B
(distribution = numerous values ---> single value
C.I. = single value --> fixed values)
Which of the following is NOT true about the standard error of a statistic?
A. The standard error measures, roughly, the average difference between the
statistic and the population parameter
B. The standard error is the estimated standard deviation of the sampling
distribution for the statics
C. The standard error can never be a negative number
D. The standard error increases as the sample size(s) increases Right Ans -
D
(s.e. & sample sz do opposite of one another)
,For a randomly elected sample of n=36 men's height, it is reported that the
standard error of the mean is 0.5 inches. Three of the following statements are
true, while one is false. Which statement is false?
A. The standard error (0.5 inches) is an estimated value of the standard
deviation of the sample mean
B. If a new sample of n= 30 men's height is collected, the standard error of the
mean might not equal 0.5 inches.
C. Over many different samples of n=36 men's heights, the average difference
between the sample means and population mean will be roughly 0.5 inches.
D. In about 95% of all samples of n= 36 men's heights, the same mean will be
within 0.5 inches of the population mean Right Ans - D
What is the primary purpose of a 95% confidence interval for a mean?
A. to estimate a sample mean
B. to test a hypothesis about a sample mean
C. to estimate a population mean
D. to provide an interval that covers 95% of the individual values in the
population Right Ans - C
(C.I. = pop mean)
The confidence level for a confidence interval for a mean is:
A. the probability the procedure provides an interval that covers the sample
mean
B. the probability of making a Type 1 error if the interval is used to test a null
hypothesis about the population mean
C. the probability that individuals in the population have values that fall into
the interval
D. the probability the procedure provides an interval that covers the
population mean Right Ans - D
Which of the following will NOT result in paired data?
A. The same measurement is taken twice on each person, under different
conditions or at different times
,B. Similar individuals are paired before giving the treatments in an
experiment. Each member of a pair then receives a different treatment. the
same response variable is measured for all individuals
C. Two different variables are measured for each individual. There is interest
in the amount of difference between the two variables
D. One random sample is taken, and a variable is recorded for each individual,
but then units are categorized as belonging to one population or another
Right Ans - D
(paired = before and after studies, non-independent)
Which of the following statements is most correct about a confidence interval
for a mean?
A. It provides a range of values, any of which is a good guess at the possible
value of the sample mean
B. It provides a range of values, any of which is a good guess at the possible
value of the population mean
C. It provides a good guess for the range of values the sample mean is likely to
have in repeated samples
D. It provides a good guess for the range of values the population mean is
likely to have in repeated samples Right Ans - B
(C.I. = pop mean)
When constructing a confidence interval for the different in two population
means, it is appropriate to use the pooled standard error only when:
A. the population standard deviations can be assumed to be equal
B. the sample standard deviations are exactly equal
C. the population means can be assumed to be equal
D. the sample means are exactly equal Right Ans - A
(pooled = same pop s.d.)
Which of the following ways of collecting data would result in two
independent samples?
, A. A sample of college students is measured for stress both before and after
taking an important exam
B. A group of college students are paired based on gender, age, and grades.
One student in a pair receives stress management training and the other one
does not. After a few weeks all students are measure for stress right before an
important exam
C. A sample of English majors is measured for stress before taking an
important exam. A sample of engineering majors is also measured for stress
before taking their important exam.
D. A sample of college students is measured for stress before taking an
important exam. Their exam grade is also recorded. Right Ans - C
Random samples of 200 men and 200 women were collected and their resting
pulse rates were measure, to estimate how much mean resting rates differ for
men and women in the population. An analyst mistakenly paired the
observations and constructed an approximate 95% confidence interval for the
mean difference to be
(5 +/- 2 x 0.2) beats per minute. If the data had been analyzed correctly,
finding an approximate 95% confidence interval of the difference in
population means, which of the following parts of the interval would be
different?
A. The sample statics of 5 beats per minute
B. The multiplier of 2
C. The standard error of 0.2
D. None of the parts would be different; it is an equivalent analysis Right
Ans - C
(multiplier is already representative of 95% C.I -->
1+ .95/ 2 --> invT: .975, 99 ~ 2
&
sample statistic is unaffected by C.I.)
A researcher asked random samples of 50 kindergarten teachers and 50 12th
grade teachers how much money they pent out-of-pocket on school supplies
in the previous school year, to see if teachers at one result, it is reasonable to
conclude that:
