Is achieving a basic skill level related to the location of the school? The results of a random sample of students by t
Posted: Wed May 11, 2022 4:01 pm
Is achieving a basic skill level related to the location of the
school? The results of a random sample of students by the location
of the school and the number of students achieving basic skill
levels in three subjects are shown in the contingency table. At
α=0.10, test the hypothesis that the variables are
independent.
(a) Identify the claim and state the null and alternative
hypotheses.
H0:
Skill level in a subject is
dependent on
independent of
location.
Ha:
Skill level in a subject is
independent of
dependent on
location.
The
alternative hypothesis
null hypothesis
is the claim.
Part 2
(b) Determine the degrees of freedom, find the
critical value, and identify the rejection region.
What are the degrees of freedom?
d.f.=
Part 3
Find the critical value.
χ2 =
(Round to three decimal places as needed.)
Part 4
Choose the correct rejection region below.
A.χ2<χ20
B.χ2≥χ20
C.χ2≤χ20
D.χ2>χ20
Part 5
(c) Calculate the test statistic. If convenient, use
technology.
χ2=enter your response here
(Round to three decimal places as needed.)
Part 6
(d) Decide to reject or fail to reject the null hypothesis.
Then interpret the decision in the context of the original
claim.
Part 7
Choose the correct conclusion below.
A.
Fail to reject
the null hypothesis. There
is not
enough evidence to reject the claim that skill level in a
subject is independent of location.
B.
Fail to reject
the null hypothesis. There
is
enough evidence to reject the claim that skill level in a
subject is independent of location.
C.
Reject
the null hypothesis. There
is
enough evidence to reject the claim that skill level in a
subject is independent of location.
D.
Reject
the null hypothesis. There
is not
enough evidence to reject the claim that skill level in a
subject is independent of location.
school? The results of a random sample of students by the location
of the school and the number of students achieving basic skill
levels in three subjects are shown in the contingency table. At
α=0.10, test the hypothesis that the variables are
independent.
(a) Identify the claim and state the null and alternative
hypotheses.
H0:
Skill level in a subject is
dependent on
independent of
location.
Ha:
Skill level in a subject is
independent of
dependent on
location.
The
alternative hypothesis
null hypothesis
is the claim.
Part 2
(b) Determine the degrees of freedom, find the
critical value, and identify the rejection region.
What are the degrees of freedom?
d.f.=
Part 3
Find the critical value.
χ2 =
(Round to three decimal places as needed.)
Part 4
Choose the correct rejection region below.
A.χ2<χ20
B.χ2≥χ20
C.χ2≤χ20
D.χ2>χ20
Part 5
(c) Calculate the test statistic. If convenient, use
technology.
χ2=enter your response here
(Round to three decimal places as needed.)
Part 6
(d) Decide to reject or fail to reject the null hypothesis.
Then interpret the decision in the context of the original
claim.
Part 7
Choose the correct conclusion below.
A.
Fail to reject
the null hypothesis. There
is not
enough evidence to reject the claim that skill level in a
subject is independent of location.
B.
Fail to reject
the null hypothesis. There
is
enough evidence to reject the claim that skill level in a
subject is independent of location.
C.
Reject
the null hypothesis. There
is
enough evidence to reject the claim that skill level in a
subject is independent of location.
D.
Reject
the null hypothesis. There
is not
enough evidence to reject the claim that skill level in a
subject is independent of location.