(a) How many capsules should a box of amoxicillin antibiotic contain? Medical research claims that 8 days of treatment with 3 tablets each day should be sufficient to kill all pathogenic bacteria. Suppose a random sample of 100 patients revealed that 10 of them have experienced relapses (i.e., not all bacteria killed and disease returned). If the alternative hypothesis is that more than 24 tablets would be required to kill all the bacteria, should the null hypothesis be rejected at α = 0.05?

(b) A manager of a firm wanted to determine if the mean daily car rental rates in Sydney is higher than that of Melbourne. He conducted a survey of 15 car rental companies in Sydney and found a sample mean of $89 and a sample standard deviation of $13. Similar survey of 12 car rental companies in Melbourne yielded a sample mean of $76 and sample standard deviation of $19. Use α = 0.01 to test whether the average daily car rental rates in Sydney is significantly higher than that in Melbourne. Assume car rental rates are normally distributed and the population variances are equal.