QUESTION SEVEN a) A cigarette manufacturingfirm distributes two brands of cigarettes. Two random samples areselected and it is found that 56 of 200 smokers prefer brand Α andthat 29 of 150 smokers prefer brandΒ . Can we conclude at the 0.05level of significance that the percentage of smokers who preferbrand Α exceeds that of brand Β by more than 10%?
b) An auditor claims that 10% of invoices for a certain companyare incorrect. To test this claim a random sample of 200 invoicesare checked and 24 are found to be incorrect. Test at the 1%significant level to see if the auditor’s claim is supported by thesample evidence.
c) The personnel department of a company developed an aptitudetest for screening potential employees. The person who devised thetest asserted that the mean mark attained would be 100. Thefollowing results were obtained with a random sample ofapplicants:
x = 96,   s= 5.2,  n=13
Test this hypothesis against the alternative that the mean markis less than 100, at the 1% significance level.
