The following data represent the level of health and the level of education for

Question

The following data represent the level of health and the level of education for a random sample of 1964 residents. Complete parts (a) and (b) below.

(a) Does the sample evidence suggest that level of education and health are independent at the

alpha

equals

0.05

level of significance?

Conduct a P-value hypothesis test. State the hypotheses. Choose the correct answer below.

A.Upper H 0: mu1equalsE1and mu2equalsE2andmu3equalsE3andmu4equalsE4

Upper H 1:At least one mean is different from what is expected.

B.Upper H 0: p1equalsp2equalsp3

Upper H 1:At least one of the proportions are not equal.

C.Upper H 0: Level of education and health are independent.

Upper H 1: Level of education and health are dependent.

Calculate the test statistic.

chi Subscript 0 Superscript 2=?

The P-value =?

Make the proper conclusion. Choose the correct answer below.

A.Fail to reject Upper H 0. There is sufficient evidence that level of education and health are associated.

B.Reject Upper H 0. There is sufficient evidence that level of education and health are associated.

C.Reject Upper H 0. There is not sufficient evidence that level of education and health are associated.

D.Fail to reject Upper H 0. There is not sufficient evidence that level of education and health are associated.

b) Construct a conditional distribution of health by level of education and draw a bar graph.

Education

Excellent          

Good

           Fair

            Poor

Not a H.S. graduate

H.S. graduate

Some college

Bachelor Degree or higher

Education Excellent Good Fair Poor Not a H.S. graduate 133 199 91 103 H.S. graduate 134 180 61 117 Some college 140 202 101 106 Bachelor Degree or higher 101 104 93 99

Explanation / Answer

Ans:

a)

H 0: Level of education and health are independent.

H 1: Level of education and health are dependent.

Expected count=row total*column total/1964

Test statistic=32.241

df=(4-1)*(4-1)=9

p-value= CHIDIST(32.241,9)=0.000181

As,p-value<0.05,reject null hypothesis.

Option B is correct.

Reject Upper H0. There is sufficient evidence that level of education and health are associated(i.e are dependent)

b)

divide each joint prob. entry by marginal prob of level of education.

e.g

P(Excellent/Not a HS graduate)=0.0677/0.2678=0.2529

Observed(O) Education Excellent Good Fair Poor Total Not a H.S. graduate 133 199 91 103 526 H.S. graduate 134 180 61 117 492 Some college 140 202 101 106 549 Bachelor Degree or higher 101 104 93 99 397 Total 508 685 346 425 1964 Expected (O) Education Excellent Good Fair Poor Total Not a H.S. graduate 136.05 183.46 92.67 113.82 526 H.S. graduate 127.26 171.60 86.68 106.47 492 Some college 142.00 191.48 96.72 118.80 549 Bachelor Degree or higher 102.69 138.46 69.94 85.91 397 Total 508 685 346 425 1964 Chi square=(O-E)^2/E Education Excellent Good Fair Poor Not a H.S. graduate 0.069 1.317 0.030 1.029 H.S. graduate 0.357 0.411 7.606 1.042 Some college 0.028 0.578 0.190 1.379 Bachelor Degree or higher 0.028 8.579 7.603 1.995 Total chi square score =32.241

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.