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STAT 2000 Assignment 5 Solutions

Question 1

Canada's last general election was held in 2011. The table below shows the proportion of voters

who supported each of the five parties:

Party

Proportion

Bloc Quebecois

0.06

Conservative

0.40

Green Party

0.04

Liberal Party

0.19

New Democratic

0.31

A sample of 500 voters was interviewed one year after the election and asked which party they

support. The results are shown in the table below:

Party

Bloc Quebecois Conservative Green Party Liberal Party New Democratic

Count

37

174

25

116

148

Expected

Cell Chi-Square

We would like to conduct a chi-square goodness of fit test at the 10% level of significance to

determine whether party support has changed in Canada since the last election.

(a) Calculate the expected cell counts and the cell chi-square values and reproduce the table above

into the answer box below. (Round all values to two decimal places.)

(b) There are no expected cell counts less than 5, so we can safely use the chi-square distribution.

What is the value of the test statistic for the appropriate test of significance (rounded to two decimal

places)?

(c) What is the P-value for the appropriate test of significance?

(d) What is the correct conclusion of the test?

(e) If we used the critical value method to conduct the test, What is the decision rule and the resulting

conclusion?

Answer Key

(a) The expected cell count for the Liberal Party is

E = 500(0.19) = 95

All other expected cell counts are calculated similarly and are shown in the table below.

The cell chi-square value for the Green Party is

All other expected cell chi-square values are calculated similarly and are shown in the table below:

Party

Bloc Quebecois Conservative Green Party Liberal Party New Democratic

Count

37

174

25

116

148

Expected

30

200

20

95

155

Cell Chi-Square

1.63

3.38

1.25

4.64

0.32

(b) The test statistic is

(c) Under the null hypothesis, the test...