Question

It is believed that cities tend to attract workers that are better educated. A sample of 610 people were classified by their highest education level (Primary and secondary school, Undergraduate and Postgraduate degree) and whether a person is working in a city or a town. The following information was obtained:

• Primary and secondary school: 89 people in total finished primary and secondary school as their highest qualification; 51 people completed their primary and secondary education and work in a city.

• Undergraduate degree: 349 people in total completed undergraduate degree as their highest qualification; 220 people completed their undergraduate degree and work in a city.

• Postgraduate degree: 172 people in total completed postgraduate degree as their highest qualification; 116 people completed their postgraduate education degree and work in a city.

a) What is the probability that a person, who has completed primary and secondary school as their highest qualification, works in a town. Show your working.

b) Let the variable Education represent the highest education level and the variable Working Status represent whether a person is working in a city or a town. Name the dependent variable.

c) We would like to investigate if there is an association between the level of education and whether a person is working in a city or town. What type of test would you conduct and why?

d) State the appropriate hypotheses statements of the test above.

e) Assume that we carry out the test above at the 1% level of significance. The test statistic value is 4.75. State the decision rule, decision, and conclusion in the context of this question. (Hint: You can use a critical value approach OR p-value approach to derive your decision

Answer 1

(a)

From the given data, the following Table iscalculated:

	primary and secondary school as their highest qualification;	undergraduate degree as their highest qualification	postgraduate education degree	Total
Working in city	51	220	116	387
Working in town	38	129	56	223
Total	89	349	172	610

P(primary and secondary school as their highest qualification AND Working in town) = 38/610 = 0.0623

So

Answer is:

0.0623

(b)

Dependent Variable: Working Status

(c)

Chi Square Test of Independence, because both the variables: Variable 1: Education : the highest education level and Variable 2: Working Status are categorical.

(d)

H0: Null Hypothesis: There is no association between the level of education and whether a person is working in a city or town

HA: Alternative Hypothesis: There is an association between the level of education and whether a person is working in a city or town (Claim)

(e)

= 0.01

df = (r - 1) X (c - 1) = (2 - 1) X (3 - 1) = 2

From Table, critical value of = 9.2103

Since calculated value of = 4.75 is less than critical value of = 9.2103, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that there is an association between the level of education and whether a person is working in a city or town.

By Technology, p - value = 0.0930

Since p - value = 0.0930 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that there is an association between the level of education and whether a person is working in a city or town.