Hypothesis Testing: Differences in Population Means1. Acme Signal Light company has decided to install new microprocessors in its traffic light assemblies and has two potential suppliers from which to choose. It would like to purchase from both in order to have more than one supply source, provided there is no difference in durability. A random sample of 35 microprocessors from Supplier A found a Mean Time to Failure of 2,800 hours. A random sample of 32 microprocessors from Supplier B found a MTF of 2,750 hours. Information from industry sources indicates that the population standard deviation is 200 hours for Supplier A and 180 hours for Supplier B. At the 5% level of significance, test the null hypothesis that the MTF is equal for these suppliers against the alternative hypothesis that there is a difference.
2. Discount stores own outlet A and outlet B. For the past year, outlet A has spent more dollars advertising widgets than outlet B. The corporation wants to know if this advertising has resulted in more sales in outlet A than in outlet B. A random sample of 36 days at outlet A had a mean of 170 widgets sold per day. A random sample of 36 days at outlet B had a mean of 165 widgets per day. Assuming population standard deviations of sales of 6 widgets at outlet A and 5 widgets at outlet B, test the null hypothesis that sales are no higher at outlet A than at outlet B against the alternative hypothesis that sales are higher at outlet A.
Hypothesis Testing: Differences in Population Proportions3. Acme Advertising was awarded a contract by a city government to communicate the need for recycling. Before their advertising campaign, survey results indicated that 36% of the cities residents believed in recycling. This survey used a sample of 50 individuals. After the campaign, a follow-up survey of 50 residents found that 24 of them believed in recycling. At the 1 percent level of significance, test the hypothesis that the campaign has not had an effect on attitudes towards recycling (i.e., that belief in recycling has not increased).
4. An automobile manufacturer wants to test whether the quality of work done in two of its assembly plants is the same. Random samples of n
1= 300 and n
2= 200 cars were taken from each plant and check for quality. The samples show 39 problems in plant 1 and 20 in plant 2. At the 1 percent significance level, test the null hypothesis that the quality of work done is the same in both plants.