Busn 5760 - Managerial Statistics

BUSN 5760

MANAGERIAL STATISTICS

ASSIGNMENT # 6

Text Chapter Covered:  9

Problem 6.1

The manager of a local branch of a bank believes that over the past few years the bank has begun to cater to a different clientele and that the average amount withdrawn from its ATMs is no longer $140.  State the null hypothesis H0 and the alternative hypothesis H1.

Problem 6.2

The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specification, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds.  A sample of 49 pieces of cloth reveals a sample mean breaking strength of 69.1 pounds.

1. State the null and alternative hypothesis.
2. Is there evidence that the machine is not meeting the manufacturer's specifications for average breaking strength? (Use a 0.05 level of significance.)
3. Compute the p-value and interpret its meaning.
4. What would your answer be in (b) if the standard deviation were specified as 1.75 pounds?
5. What would be your answer in (b) if the sample mean were 69 pounds and the standard deviation is 3.5 pounds?

Problem 6.3

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line.  The machine that dispenses dressings is working properly when 8 ounces are dispensed.  The standard deviation is 0.15 ounce.  A sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces.  Suppose that the mean amount dispensed in a particular sample of 50 bottles is 7.983 ounces.

1. State the null and alternate hypotheses.
2. Is there evidence that the population average amount is different from 8 ounces? (use a 0.05 level of significance.)
3. Compute the p-value and interpret its meaning.
4. What will be your answer in (b) if the standard deviation is specified as 0.05 ounce?
5. What will be your answer in (b) if the sample mean is 7.952 ounces and the standard deviation is 0.15 ounce?

Problem 6.4

A manufacturer of salad dressings uses machines to dispense liquid into bottles that move along a filling line.  The machine that dispenses dressing is working properly when 8 ounces are dispensed.  The manufacturer is particularly concerned that the bottles do not have an average of less than 8 ounces.  The standard deviation of the process is 0.15 ounce.  A sample of 50 bottles is selected periodically and the filling line is stopped if there is evidence that the mean amount dispensed is actually less than 8 ounces.  Suppose that the average amount dispensed in a particular sample of 50 bottles is 7.983 ounces.

1. State the null and alternate hypotheses.
2. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the mean amount dispensed is less than 8 ounces?
3. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence that the mean amount dispensed is less than 8 ounces?
4. Interpret the meaning of the p-value in this problem.
5. Compare your conclusions in (b) and (c).

Problem 6.5

The policy of a particular bank branch is that its ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend.  Customer goodwill depends on such services meeting customer needs.  At this branch the expected (i.e. population) mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with an expected (i.e. population) standard deviation of $30.  Suppose that a random sample of 36 customer transactions is examined, and it is observed that the sample mean withdrawal is $172.