A random sample of 395 people were surveyed and each person was asked to report

Question

A random sample of 395 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table Female Male Total High SchoolBachelorsMasters Ph.D.Total 201 194 395 46 54 100 40 56 96 62 53 102 97 A) This sample has degree of freedom: If gender and highest education level are independent, then B) Accurate to 2 decimal places, the expected count in row 2 column 3 is ? C) Accurate to 2 decimal places, the component value in row 2 column 3 of the table is component2,3- D) x value of this sample is ? E) At significance level 0.01, is the sample showing strong evidence that gender and highest education level are dependent? Use 4 decimal places for p-value. Yes ONo F) The p-value of this sample was

Explanation / Answer

Ans:

a)

DF=(2-1)*(4-1)=3

b)Expected count=100*194/395=49.11

c)Chi square contribution=(54-49.11)^2/49.11=0.49

d)Chi square score=5.50

e)p-value=CHIDIST(5.50,3)=0.1386

As,p-value>0.01,we fail to reject null hypothesis.There is not sufficient evidenec to conclude that gender and highest education level are dependent.

Observed(fo) High school Bachelors Maters Ph.D Total Female 62 53 46 40 201 Male 40 44 54 56 194 Total= 102 97 100 96 395 Expected(fe) High school Bachelors Maters Ph.D Total Female 51.90 49.36 50.89 48.85 201 Male 50.10 47.64 49.11 47.15 194 Total= 102 97 100 96 395 Chi square=(fo-fe)^2/fe High school Bachelors Maters Ph.D Total Female 1.96 0.27 0.47 1.60 2.70 Male 2.03 0.28 0.49 1.66 2.80 Total= 4.00 0.55 0.96 3.26 5.50

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