Question 1

In a broad sense, the role of a confidence interval for the population mean is meant to accurately portray what?

Accepted Answer

A)   If you take a random sample, the sample mean is a biased estimate of the population mean.
B)   Different population distributions have different population means.
C)   The uncertainty involved with observing a sample and not the entire population.
D)   None of the answers is correct. C

Question 2

As the size of a random sample gets larger, what does the distribution of the sample mean begin to resemble?

Accepted Answer

A)   The underlying population distribution
B)   A t-statistic
C)   A normal distribution
D)   None of the answers is correct. C

Question 3

Which of the following is not a required assumption in the reasoning behind constructing a hypothesis test of a population mean?

Accepted Answer

A)   The population mean is K.
B)   The size of the sample is sufficiently large .
C)   The population distribution is normal.
D)   The data sample is random. C

Question 4

What sample statistic is not likely to be used to construct a confidence interval of a population mean?

Accepted Answer

A)   Sample mean
B)   Sample standard deviation
C)   Number of observations
D)   Sample range

Question 5

If you were building a hypothesis test to determine whether or not the price elasticity of demand for your product is -3.0, which of the following would be a natural null hypothesis?

Accepted Answer

A)   H0: Price Elasticity of Demand = 0
B)   H0: Price Elasticity of Demand = 1
C)   H0: Price Elasticity of Demand = -3.0
D)   H0: Price Elasticity of Demand = -1

Question 6

Suppose a sample of five econometrics students' heights were: 69 inches, 73 inches, 65 inches, 67 inches, and 71 inches. What is the sample mean of the height of the students?

Accepted Answer

A)   71 inches
B)   68 inches
C)   68.5 inches
D)   69 inches

Question 7

A range of values such that there is a specified probability that they contain a population parameter is known as a(n):

Accepted Answer

A)   unbiased estimator.
B)   sample mean.
C)   confidence interval.
D)   random sample.

Question 8

In making an active prediction that using a large banner advertisement will increase click-through rates based on a sample of data, what is not an appropriate criticism that someone might have for your prediction?

Accepted Answer

A)   That your sample was not randomly selected.
B)   That you do not have a large enough sample.
C)   That the underlying population distribution is not normal.
D)   That you used a sample of data to make a prediction about the population.

Question 9

Suppose you have a random sample of 21 credit scores from a population of mortgage applicants with a sample mean of 620 and sample standard deviation of 70, and would like to calculate the 99 percent confidence interval of the population mean credit score. Which of the following would be the correct construction?

Accepted Answer

A)   620 ± 2.58  (7021) \left( \frac { 70 } { \sqrt { 21 } } \right) (21c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​70​)  
B)   620 ± 4  (7021) \left( \frac { 70 } { \sqrt { 21 } } \right) (21c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​70​)   , because 4 is the t-distribution critical value.
C)   620 ± 4 (70) , because 4 is the t-distribution critical value.
D)   None of these choices are correct.

Question 10

As long as your sample is large enough, you don't have to worry about using the sample standard deviation in place of the unknown population standard deviation in constructing a confidence interval because ________.

Accepted Answer

A)   for low degrees of freedom, the t-distribution is similar to the standard normal distribution
B)   for all degrees of freedom, the t-distribution is bell-shaped
C)   for a large sample, the t-distribution is similar to the standard normal distribution
D)   the sample standard deviation is an efficient estimator of the population standard deviation

Question 11

A convenient way to modify your degree of support for a decision on a hypothesis test is to calculate the ________ in conjunction with test statistic?

Accepted Answer

A)   P-value
B)   Standard error
C)   Sample standard deviation
D)   Unbiased estimator

Question 12

A hypothesis to be tested using a data sample is known as:

Accepted Answer

A)   the null hypothesis.
B)   the true hypothesis.
C)   the unbiased hypothesis.
D)   the population hypothesis.

Question 13

If you conduct a hypothesis test under the scenario in which you know the population standard deviation, which of the following will not affect the size of the p-value of the hypothesis test?

Accepted Answer

A)   Sample mean
B)   Null hypothesis population mean
C)   Sample standard deviation
D)   Whether the hypothesis is one or two sided

Question 14

To use the normal distribution to calculate the p-value of a hypothesis test involving the population mean, which assumption is not necessary?

Accepted Answer

A)   The sample is random.
B)   The null hypothesis is zero.
C)   The sample is "large" enough .
D)   None of the answers is correct.

Question 15

Suppose you had a random sample of 50 observations with a sample mean of 10 and sample standard deviation of 5. Suppose another observation is observed that has a value of 10. How will the sample mean change from the original sample?

Accepted Answer

A)   It will not change.
B)   It will increase.
C)   It will decrease.
D)   Cannot be determined by the information given.

Question 16

A random variable that can only take on a countable number of values is known as what type of random variable?

Accepted Answer

A)   Discrete
B)   Continuous
C)   Population parameter
D)   Probability density function

Question 17

In principle, why are t-statistics and critical values not as useful in the practical construction of confidence intervals in most applications?

Accepted Answer

A)   Their use is only valid in large samples.
B)   Their use is only valid in small samples.
C)   They are not often found in most software applications.
D)   In large samples (i.e., large degrees of freedom)  the t-distribution and standard normal distribution are very similar.

Question 18

For the same sample, the 95% confidence interval will have what relation to the 99% confidence interval?

Accepted Answer

A)   It will be larger.
B)   It will be smaller.
C)   They will not overlap.
D)   They will be exact complements of each other.

Question 19

Suppose a sample of five retail stores' monthly profits are: $4,000, $7,000, $5,000, $3,000, and $1,000. What will the sample variance of stores profits be?

Accepted Answer

A)   $20 million
B)   $4 million
C)   $10 million
D)   $5 million

Question 20

Suppose you have a random sample of 2,179 credit scores from a population of mortgage applicants with a sample mean of 620 and sample standard deviation of 70, and would like to calculate the t-stat for the null hypothesis that the population mean is 610. Which of the following is the correct construction of the t-stat?

Accepted Answer

A)    620−61070/2179\frac { 620 - 610 } { 70 / \sqrt { 2179 } }70/2179c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​620−610​ 
B)    620−61070\frac { 620 - 610 } { 70 }70620−610​ 
C)    62070/2179\frac { 620 } { 70 / \sqrt { 2179 } }70/2179c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​620​ 
D)    610−62070/2179\frac { 610 - 620 } { 70 / \sqrt { 2179 } }70/2179c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​610−620​

Exam 3: Reasoning From Sample to Population