1)The average years of employee experience at any company is normally distributed, with a standard deviation of 12 years. If a sample of 50 employees indicates a mean age is 38 year.
a)Calculate a 90% confidence interval for the population mean.
b) How many employees should we sample if we want to change the ME to 2.5 with 90% confidence?
c)Calculate a 99% confidence interval for the population mean.
d)How many employees should we sample if we want to change the ME to 3.9 with 99% confidence?
2)A labor union has several thousand members. In a sample of 40 union members, 32 have indicated that they are in favor of accepting the union's current compensation plan. Calculate 99 percent confidence intervals for the population proportion of members who are in favor of the plan.
3)Safe Lumber Company hires an independent contractor to monitor the groundwater within a one mile radius of its factory to ensure that no toxic levels of arsenic are being released. The contractor takes a sample of groundwater from selected sites within the one mile radius.
a)Suppose that data from 25 sites had arsenic levels averaging 75 ppb with a sample SD of 30 ppb. Construct a 95% confidence interval for the arsenic level.
b)Suppose that data from 9 sites had arsenic levels averaging 75 ppb with a sample SD of 30 ppb. Construct a 95% confidence interval for the arsenic level.
4)Borrowers Bank classifies credit cardholders as "prime" whenever they pay interest charges for at least 6 of the last 12 billing cycles. The table below cross classifies 2080 cardholders according to whether they are 1) prime or not, and 2) below age 30 or not
|
|
Below 30
|
30 and Over
|
|
Prime
|
475
|
510
|
|
Not Prime
|
376
|
719
|
a)Construct a 95% confidence interval for the percentage of Prime cardholders among those who are less than 30 years old.
b) Construct a 95% confidence interval for the percentage of Prime cardholders among those who are 30 years or older.