Question 1

The Rutter Nursery Company packages its mulch in 50 kg bags. From a long history, the shipping department reports that the distribution of the bag masses follows the normal distribution and the standard deviation of this process is 3 kg per bag. At the end of each day, Jeff Rutter, the shipping manager, selects 10 bags and computes the mean mass of the sample. The sample mean was found to be 48.18 kg.

a)Can Mr. Rutter conclude that the mean mass of the bags is less than 50 kg? Use the 1% significance level.

b)Calculate the pvalue.

Question 2

In recent years, the interest rates on home mortgages have declined to less than 6%. However, a recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level of significance, is it reasonable to conclude the mean rate charged is greater than 14%?

Question 3

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?