Question

# 3.5 - A recent census asked respondents to state the highest level of education that they...

3.5 - A recent census asked respondents to state the highest level of education that they had received. The responses were 39% High school, 45% TAFE or Undergraduate Degree, 13% Higher Degree and 3% Other.

The mayor of a small country town held a similar survey. Below are observed counts for each of the education levels for 250 respondents from the town: Highest Education Level

 Highest education level Observed count High school 115 Tafe or uni 105 Higher degree 20 Other 10

a) If the counts observed for the town matched that of the census, what would be the expected counts for

each education level?

b) To see if these results are unusual, should you perform a goodness-of-fit test or a test of independence?

d) How many degrees of freedom are there?

e) Find x2 and the P-value.

f) State your conclusion (use α = 0.05) in the context of the question.

Show all working out and dont no technology (ie. spss or excel)

a) The following table is obtained:

 Categories Observed Expected (fo-fe)2/fe High School 115 250*0.39=97.5 (115-97.5)2/97.5 = 3.141 Tafe or Uni 105 250*0.45=112.5 (105-112.5)2/112.5 = 0.5 Higher degree 20 250*0.13=32.5 (20-32.5)2/32.5 = 4.808 Other 10 250*0.03=7.5 (10-7.5)2/7.5 = 0.833 Sum = 250 250 9.282

b) we should perform a goodness-of-fit test.

c) Null and Alternative Hypotheses:

H0​: p1​=0.39, p2​=0.45, p3​=0.13, p4​=0.03

Ha​: Some of the population proportions differ from the values stated in the null hypothesis.

d) Degree of freedom = 4-1=3

e) Test statistic:

p-value = CHISQ.DIST.RT(9.282, 3) = 0.0257

f) p-value < α, Reject the null hypothesis.

There is enough evidence to conclude that the population proportions differ from the values stated in the null hypothesis.

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