Question

QUESTION 4 (2 + 1 + 2 + 1 + 4 =10 marks)

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.

1. 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.

2. 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.

3. 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?

4. State the appropriate hypotheses statements of the test above.

5. 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

Answer:-

Given That:-

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.

Given,

	Does Work	Does not work	Total
Primary and secondary education	51	38	89
Undergraduate degree	220	129	349
Posrgraduate degree	116	56	172
Total	387	223	610

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.

Probability = 51/89 = 0.57

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.

The dependent variable is the working status.

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?

The chi-square test of association would be appropriate here because we have two categorical variables.

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

The hypothesis being tested is:

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

Ha: There is an association between the level of education and whether a person is working in a city or town.

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)

Decision rule:

Reject H0 if the p-value < 0.01.

	Does Work	Does not work	Total
Primary and secondary education Observed Expected O - E	51 56.46 -5.46 0.53	38 32.54 5.46 0.92	89 89.00 0.00 1.45
Undergraduate degree Observed Expected O - E	220 221.41 -1.41 0.01	129 127.59 1.41 0.02	349 349.00 0.00 0.02
Posrgraduate degree Observed Expected O - E	116 109.12 6.88 0.43	56 62.88 -6.88 0.75	172 172.00 0.00 1.19
Total Observed Expected O - E	387 387.00 0.00 0.97	223 223.00 0.00 1.69	610 610.00 0.00 4.75
	4.75 2 .2649	chi-square df p - value

The p-value is 0.2649.

Since the p-value (0.2649) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is an association between the level of education and whether a person is working in a city or town.

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