A study was performed to determine if there is a relationship between gender and

Question

A study was performed to determine if there is a relationship between gender and whether or not people exercise.

20 subjects were selected at random, their gender (M = Male, F = Female) was recorded and whether or not they exercised

(Y = Yes, N = No).

The results from the measurements are summarised below: Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Gender M F M F M M M F F M F M M F F F M M F M Exercise Y N N Y N Y N Y Y Y N N Y Y N Y N N Y N

1. What type of study is outlined here? Justify your answer. [2 marks]

2. What are the data types and scale of measurement of each measurement? [2 marks]

3. Summarise the data in a contingency table. [9 marks]

4. If a subject is selected at random, what is the probability that the subject will be male? [2 marks]

5. If a subject is selected at random, what is the probability that the subject will be female and exercise? [2 marks]

6. Use a 0.10 significance level and the following points to test the claim that there is no association between gender and whether or not people exercise.

(a) State the null and alternative hypotheses in context. [5 marks]

(b) Calculate the test statistic. [8 marks]

(c) Identify the rejection region(s). [5 marks]

(d) Clearly state your conclusions (in context). [5 marks]

Explanation / Answer

1)

This is an observational study.

2)

Both gender and exercise are categorical data.

3)

4)

P(Male|Total)=11/20= 0.55

5)

P(F&E|Total)=6/20=0.3

Do exercise No exercise Total Male 4 7 11 Female 6 3 9 Total 10 10 20

4)

P(Male|Total)=11/20= 0.55

5)

P(F&E|Total)=6/20=0.3

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