Question

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?

c) State your hypotheses.

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)

Answer 1

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.