A recent survey indicated that 54% of employed Canadians admit that they have ta

Question

A recent survey indicated that 54% of employed Canadians admit that they have taken a sick day when they were not really sick. The survey results suggest that there marked differences in this percentage among the provinces. A random sample of 400 employed Canadians from Quebec (a province) was selected and 240 admitted that they have faked an illness.

a. Conduct a hypothesis test to test the claim that the population proportion of "fakers" is different for Quebec then for the whole of Canada at the 5% significance level. Be sure to state you Ho and Ha, your test statistic and p-value, whether or not you reject Ho and whether you support the claim.

b. Write a complete sentence describing what a Type I error is in context.

c. Write a complete sentence describing what a Type II error is in context.

Explanation / Answer

Ans:

a)

H0:p is equal to 0.54

Ha:p is not equal to 0.54

sample proportion=240/400=0.6

Test statistic:

z=(0.6-0.54)/sqrt(0.54*(1-0.54)/400)

z=2.41

p-value=2*P(z>2.41)=0.0160

As,p-value<0.05,we reject null hypothesis.There is sufficient evidence to support the claim that population proportion of fakers is different from 0.54.

b)When we conclude that population proportion of fakers is different from 0.54,but in actual it is equal to 0.54,then we will make type I error.

c)When we conclude that population proportion of fakers is equal to 0.54,but in actual it is different from 0.54,the we will make type II error.

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