perform a chi squared test to see whether there is evidence of a significant dif

Question

perform a chi squared test to see whether there is evidence of a significant difference among all the different countries mentioned with respect to the proportion of companies who have at least one female director on their boards. Use 0.05 significance level.

Question 1

State the null and alternative hypotheses.

Question 2

How many degrees of freedom are in this test?

Question 3

What is the critical value of chi squared? (please answer with at least 4 significant figures)

Question 4

What is the test chi squared statistic? (please answer with at least 4 significant figures)

Question 5

What is the p-value of this chi-squared test? (please answer to at least 4 decimal places)

Question 6

We reject the null hypothesis.

Select one:

True

False

Question 7

What is the conclusion of the chi square test?

Select one:

a. There is evidence of a significant difference among the countries with respect to the proportion of companies who have at least one female director on their boards.

b. There is not enough evidence of a significant difference among the countries with respect to the proportion of companies who have at least one female director on their boards

Question 8

Why did you come to this conclusion? Be specific about the decision rule you used.

The GMI Ratings' 2012 Women on Boards Survey showed incremental improvements in most measures of female board representation in the past year. The study reported that 90 of 101 (89%) of French companies sampled, 136 of 197 (69%) of Australian companies sampled, 26 of 28 (93%) of Norwegian companies sampled, 27 of 53 (51%) of Singaporean companies, and 95 of 134 (71%) of Canadian companies sampled have at least one female director on their boards. (Data extracted from bit.lylzBAnYv.)

Explanation / Answer

null hypothesis: seecting at least one female director on their boards and country selected is independent of each other.

Alternate Hypothesis: they are not independent

2) degree of freedom =(row-1)(column-1) =(2-1)(5-1) =4

3) for 4 df and at 0.05 level of 0.05 significanfce level , critical value of chi square=9.488

4)test statistic for above =33.775

5) p-value of this chi-squared test =0.0000

6)We reject the null hypothesis: true

7). There is evidence of a significant difference among the countries with respect to the proportion of companies who have at least one female director on their boards.

8) as p value is low then 0.05 level, and test stat is higher then critical value.

Observed O french American Norwegian Singapore Canadian Total have at least one Female 90 136 26 27 95 374 Have none 11 61 2 26 39 139 Total 101 197 28 53 134 513 Expected E=rowtotal*column total/grand total french American Norwegian Singapore Canadian Total have at least one Female 73.634 143.622 20.413 38.639 97.692 374 Have none 27.366 53.378 7.587 14.361 36.308 139 Total 101 197 28 53 134 513 chi square =(O-E)^2/E french American Norwegian Singapore Canadian Total have at least one Female 3.638 0.404 1.529 3.506 0.074 9.152 Have none 9.788 1.088 4.114 9.434 0.200 24.624 Total 13.426 1.493 5.643 12.940 0.274 33.775

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