Question

A survey of 36 randomly selected students who dropped a course was conducted at a college. The following results were collected. Complete parts​ (a) through​ (c).

a) Construct a contingency table for the two variables.

	CourseCourse	PersonalPersonal	WorkWork
Male
FemaleFemale

​(b) Test whether gender is independent of drop reason at the

alphaαequals=0.1

level of significance.

What are the​ hypotheses?

A.

Upper H 0H0​:

pSubscript Upper CCequals=pSubscript Upper PPequals=pSubscript Upper WW

Upper H 1H1​:

At least one of the proportions is different from the others.

B.

Upper H 0H0​:

Gender and drop reason are independent.

Upper H 1H1​:

Gender and drop reason are dependent.

C.

Upper H 0H0​:

OSubscript Upper CCequals=ESubscript Upper CC

and

OSubscript Upper PPequals=ESubscript Upper PP

and

OSubscript Upper WWequals=ESubscript Upper WW

Upper H 1H1​:

OSubscript Upper CCnot equals≠ESubscript Upper CC

or

OSubscript Upper PPnot equals≠ESubscript Upper PP

or

OSubscript Upper WWnot equals≠ESubscript Upper WW

Calculate the test statistic.

chi Subscript 0 Superscript 2χ20equals=nothing

​(Round to three decimal places as​ needed.)

Determine the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

Make the proper conclusion. Choose the correct answer below.

A.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

sufficient evidence that gender and drop reason are dependent.

B.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence that gender and drop reason are dependent.

C.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not

sufficient evidence that gender and drop reason are dependent.

D.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence that gender and drop reason are dependent.

​(c) Construct a conditional distribution of drop reason by gender. Fill in the table below.

	CourseCourse	PersonalPersonal	WorkWork
Male	nothing	nothing	nothing
FemaleFemale	nothing	nothing	nothing

​(Round to three decimal places as​ needed.)

Choose the correct bar graph below.

A.

A side-by-side bar graph has a vertical axis labeled from 0 to 1 in increments of 0.2 and a horizontal axis labeled from left to right with the words "Male" and "Female." The bar graph contains 3 vertical bars above each horizontal axis label; the 3 bars within each set are labeled from left to right as follows: "C," "P," "W." From left to right, the vertical bars in each set have approximate heights as follows, where for each set the horizontal axis label is listed first and individual bar heights are listed from left to right: "Male," 0.38, 0.46, 0.32; "Female," 0.16, 0.32, 0.4. 01MaleFemaleCPWCPW

B.

A side-by-side bar graph has a vertical axis labeled from 0 to 1 in increments of 0.2 and a horizontal axis labeled from left to right with the words "Male" and "Female." The bar graph contains 3 vertical bars above each horizontal axis label; the 3 bars within each set are labeled from left to right as follows: "C," "P," "W." From left to right, the vertical bars in each set have approximate heights as follows, where for each set the horizontal axis label is listed first and individual bar heights are listed from left to right: "Male," 0.32, 0.32, 0.38; "Female," 0.4, 0.46, 0.16. 01MaleFemaleCPWCPW

C.

A side-by-side bar graph has a vertical axis labeled from 0 to 1 in increments of 0.2 and a horizontal axis labeled from left to right with the words "Male" and "Female." The bar graph contains 3 vertical bars above each horizontal axis label; the 3 bars within each set are labeled from left to right as follows: "C," "P," "W." From left to right, the vertical bars in each set have approximate heights as follows, where for each set the horizontal axis label is listed first and individual bar heights are listed from left to right: "Male," 0.4, 0.46, 0.16; "Female," 0.32, 0.32, 0.38. 01MaleFemaleCPWCPW

Gender   Reason
F   Course
M   Work
F   Work
M   Personal
F   Personal
M   Personal
M   Course
F   Personal
F   Personal
F   Personal
F   Work
M   Work
M   Work
F   Course
M   Work
F   Course
M   Personal
F   Personal
F   Work
M   Course
F   Course
M   Course
M   Work
F   Course
F   Personal
F   Course
M   Personal
F   Course
F   Personal
M   Course
M   Course
M   Personal
M   Work
F   Course
F   Personal
F   Personal

Answer 1

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ANSWER:

a.

	Course	Personal	Work
Male	4	5	6
Female	8	9	4

b. H0: gender is independent of drop reason.

H1:gender is not independent of drop resaon.

c. Compute X^2 test of independence for the given data.

Observed	Expected, fe=row marginal*column marginal/Total	(Observed-Expected)^2/Expected
4	5 [(15*12)/36]	0.2 [(4-5)^2/5]
5	5.833	0.1190
6	4.167	0.8067
8	7	0.1429
9	8.167	0.0850
4	5.833	0.5762
		X^2=sigma (Observed-Expected)^2/Expected =1.930

d. p value at 2 df [df=(row-1)(column-1)] is 0.381.

e. Reject H0, if p value is less than 0.1. Here, fail to reject H0, p>0.1, and conclude that there is insufficient evidence to cocnclude that gender is not independent of drop reason.

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