Question

A study was made of 147 industrial accidents that required medical attention. A researcher claims that the accidents occur with equal proportions on the 5 workdays. If the test statistic χ² = 10.65 and the critical value χ² (4)= 9.49, then

		fail to reject the claim that the accidents occur with equal proportions on the 5 workdays
		accept the claim that the accidents occur with equal proportions on the 5 workdays
		reject the claim that the accidents occur with equal means on the 5 workdays
		reject the claim that the accidents occur with equal proportions on the 5 workdays

Answer 1

Let the actual population proportion of accidents in i th day out of the 5 working days be pi, i=1,2,3,4,5.

Then here we are to test :

Null hypothesis, H: p1=p2=...=p5

Versus alternative hypothesis, K: H is not true.

This is a standard testing problem and for this testing we use chi-square test procedure.

This is a right tailed test, i.e. we reject the null hypothesis at a specific level if the observed test statistic is more than the critical value at that specified size.

Here observed test statistic is χ² = 10.65

And the critical value χ²(4)= 9.49.

Clearly χ² is more than the critical value.

Hence we reject our null hypothesis in favour of the alternative hypothesis.

That is, reject the claim that the accidents occur with equal proportions on the 5 workdays.

so last option is the correct one.

The other options are incorrect for obvious reasons.

Hope the solution helps. Thank you.