Course: MAT-240
Assignment: 5-2 MyStatLab: Module
Week Five Problem Set
1. Determine whether the following sampling is dependent or independent. Indicate
whether the response variable is qualitative or quantitative.
A researcher wishes to compare mental health of married lawyers and their spouses. She
obtains a random sample of 406 such couples who take a mental health inventory and
determines each spouses mental health.
Determine whether the following sampling is dependent or independent.
A. The sampling is dependent because an individual selected for one sample
does not dictate which individual is to be in the second sample.
B. The sampling is dependent because an individual selected for one sample
does dictate which individual is to be in the second sample.
C. The sampling is independent because an individual selected for one
sample does not dictate which individual is to be in the second sample.
D. The sampling is independent because an individual selected for one
sample does dictate which individual is to be in the second sample.
Indicate whether the response variable is qualitative or quantitative.
A. The variable is qualitative because it classifies the individual.
B. The variable is quantitative because it classifies the individual.
C. The variable is quantitative because it is a numerical measure.
D. The variable is qualitative because it is a numerical measure.
Notes:
By definition, a sampling method is independent when an individual selected for
one sample does not dictate which individual is to be in the second sample.
Conversely, a sampling method is dependent when an individual selected for one
sample does dictate which individual is to be in the second sample.
Qualitative variables allow for classification of individuals based on some
attribute or characteristic. Quantitative variables provide numerical measures of
individuals, and can be added or subtracted.
,2. An educator wants to determine whether a new curriculum significantly improves
standardized test scores for students. She randomly divides 90 students into two groups. Group
1 is taught using the new curriculum, while group 2 is taught using the traditional curriculum. At
the end of the school year, both groups are given the standardized test and the mean scores
are compared. Determine whether the sampling is dependent or independent. Indicate whether
the response variable is qualitative or quantitative.
Determine whether the sampling is dependent or independent.
A. The sampling is dependent because the individuals selected to be in one
sample are used to determine the individuals to be in the second sample.
B. The sampling is independent because the individuals selected to be in
one sample are used to determine the individuals to be in the second sample.
C. The sampling is dependent because the individuals selected for one
sample do not dictate which individuals are to be in a second sample.
D. This sampling is independent because the individuals selected for one
sample do not dictate which individuals are to be in a second sample.
Indicate whether the response variable is qualitative or quantitative.
A. The variable is quantitative because it classifies the individual.
B. The variable is qualitative because it classifies the individual.
C. The variable is qualitative because it is a numerical measure.
D. The variable is quantitative because it is a numerical measure.
Notes:
By definition, a sampling method is independent when an individual selected for
one sample does not dictate which individual is to be in the second sample.
Conversely, a sampling method is dependent when an individual selected for one
sample does dictate which individual is to be in the second sample.
Qualitative variables allow for classification of individuals based on some
attribute or characteristic. Quantitative variables provide numerical measures of
individuals, and can be added or subtracted.
,3. Conduct a test at the α = 0.05 level of significance by determining (a) the null and
alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were
obtained independently from a large population using simple random sampling.
Test whether p1 > p2. The sample data are:
x1 = 129, n1 = 245, x2 = 139, and n2 = 302
(a) Choose the correct null and alternative hypotheses below.
A. H0 : p1 = p2 versus H1 : p1 ≠ p2
B. H0 : p1 = p2 versus H1 : p1 > p2
C. H0 : p1 = p2 verses H1 : p1 < p2
D. H0 : p1 = 0 versus H1 : p1 ≠ 0
Notes:
H0 will ALWAYS have both proportions equal. We always assume that the
proportions have no difference for the null.
H1 will compare p1 and p2, but you need to figure out if it is left (<), right (>), or
two tailed (not equal).
(b) Determine the test statistic.
z0 = 1.54
(Round to two decimal places as needed.)
(c) Determine the P-value.
The P-value is 0.062
(Round to three decimal places as needed.)
Notes:
Stat → Proportion Stat → Two Sample → With Summary
x1 = successes, n1 = observations
x2 = successes, n2 = observations
Choose hypothesis test
For hypothesis test:
z stat is the test statistic
P-value is next to that figure.
, What is the result of this hypothesis test?
A. Reject the null hypothesis because there is sufficient evidence to
conclude that p1 < p2.
B. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 > p2.
C. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 < p2.
D. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 ≠ p2.
Notes:
Assignment: 5-2 MyStatLab: Module
Week Five Problem Set
1. Determine whether the following sampling is dependent or independent. Indicate
whether the response variable is qualitative or quantitative.
A researcher wishes to compare mental health of married lawyers and their spouses. She
obtains a random sample of 406 such couples who take a mental health inventory and
determines each spouses mental health.
Determine whether the following sampling is dependent or independent.
A. The sampling is dependent because an individual selected for one sample
does not dictate which individual is to be in the second sample.
B. The sampling is dependent because an individual selected for one sample
does dictate which individual is to be in the second sample.
C. The sampling is independent because an individual selected for one
sample does not dictate which individual is to be in the second sample.
D. The sampling is independent because an individual selected for one
sample does dictate which individual is to be in the second sample.
Indicate whether the response variable is qualitative or quantitative.
A. The variable is qualitative because it classifies the individual.
B. The variable is quantitative because it classifies the individual.
C. The variable is quantitative because it is a numerical measure.
D. The variable is qualitative because it is a numerical measure.
Notes:
By definition, a sampling method is independent when an individual selected for
one sample does not dictate which individual is to be in the second sample.
Conversely, a sampling method is dependent when an individual selected for one
sample does dictate which individual is to be in the second sample.
Qualitative variables allow for classification of individuals based on some
attribute or characteristic. Quantitative variables provide numerical measures of
individuals, and can be added or subtracted.
,2. An educator wants to determine whether a new curriculum significantly improves
standardized test scores for students. She randomly divides 90 students into two groups. Group
1 is taught using the new curriculum, while group 2 is taught using the traditional curriculum. At
the end of the school year, both groups are given the standardized test and the mean scores
are compared. Determine whether the sampling is dependent or independent. Indicate whether
the response variable is qualitative or quantitative.
Determine whether the sampling is dependent or independent.
A. The sampling is dependent because the individuals selected to be in one
sample are used to determine the individuals to be in the second sample.
B. The sampling is independent because the individuals selected to be in
one sample are used to determine the individuals to be in the second sample.
C. The sampling is dependent because the individuals selected for one
sample do not dictate which individuals are to be in a second sample.
D. This sampling is independent because the individuals selected for one
sample do not dictate which individuals are to be in a second sample.
Indicate whether the response variable is qualitative or quantitative.
A. The variable is quantitative because it classifies the individual.
B. The variable is qualitative because it classifies the individual.
C. The variable is qualitative because it is a numerical measure.
D. The variable is quantitative because it is a numerical measure.
Notes:
By definition, a sampling method is independent when an individual selected for
one sample does not dictate which individual is to be in the second sample.
Conversely, a sampling method is dependent when an individual selected for one
sample does dictate which individual is to be in the second sample.
Qualitative variables allow for classification of individuals based on some
attribute or characteristic. Quantitative variables provide numerical measures of
individuals, and can be added or subtracted.
,3. Conduct a test at the α = 0.05 level of significance by determining (a) the null and
alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were
obtained independently from a large population using simple random sampling.
Test whether p1 > p2. The sample data are:
x1 = 129, n1 = 245, x2 = 139, and n2 = 302
(a) Choose the correct null and alternative hypotheses below.
A. H0 : p1 = p2 versus H1 : p1 ≠ p2
B. H0 : p1 = p2 versus H1 : p1 > p2
C. H0 : p1 = p2 verses H1 : p1 < p2
D. H0 : p1 = 0 versus H1 : p1 ≠ 0
Notes:
H0 will ALWAYS have both proportions equal. We always assume that the
proportions have no difference for the null.
H1 will compare p1 and p2, but you need to figure out if it is left (<), right (>), or
two tailed (not equal).
(b) Determine the test statistic.
z0 = 1.54
(Round to two decimal places as needed.)
(c) Determine the P-value.
The P-value is 0.062
(Round to three decimal places as needed.)
Notes:
Stat → Proportion Stat → Two Sample → With Summary
x1 = successes, n1 = observations
x2 = successes, n2 = observations
Choose hypothesis test
For hypothesis test:
z stat is the test statistic
P-value is next to that figure.
, What is the result of this hypothesis test?
A. Reject the null hypothesis because there is sufficient evidence to
conclude that p1 < p2.
B. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 > p2.
C. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 < p2.
D. Do not reject the null hypothesis because there is not sufficient evidence
to conclude that p1 ≠ p2.
Notes:
