Question

QUESTION SEVEN a) A cigarette manufacturing firm distributes two brands of cigarettes. Two random samples are selected and it is found that 56 of 200 smokers prefer brand Α and that 29 of 150 smokers prefer brandΒ . Can we conclude at the 0.05 level of significance that the percentage of smokers who prefer brand Α exceeds that of brand Β by more than 10%?

b) An auditor claims that 10% of invoices for a certain company are incorrect. To test this claim a random sample of 200 invoices are checked and 24 are found to be incorrect. Test at the 1% significant level to see if the auditor’s claim is supported by the sample evidence.

c) The personnel department of a company developed an aptitude test for screening potential employees. The person who devised the test asserted that the mean mark attained would be 100. The following results were obtained with a random sample of applicants:

x = 96,   s= 5.2,   n=13

Test this hypothesis against the alternative that the mean mark is less than 100, at the 1% significance level.

Answer 1

a) Let denote the true proportion of smokers who prefer brand A and brand B respectively.

b) Let p denotes the true proportion of of invoices for a certain company that are incorrect.

So, we can say that there is sufficient evidence to support the auditor’s claim.

c) Let denotes the true mean mark attained.