Q1.

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, ?, spent by customers at the supermarkets has been reported to be 38 minutes, but executives have good reason to believe that ? is greater than 38 minutes. The executives hire a statistical consultant and ask her to perform a statistical test.

To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 45 minutes and the standard deviation of the times to be 12

minutes.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be making?
	?(Choose one)
(c)	Suppose the true mean shopping time spent by customers at the supermarkets is 38 minutes. Fill in the blanks to describe a Type I error.
A Type I error would be ?(Choose one - Type 1, Type 2 ) the hypothesis that ? is ?(Choose one - rejecting, failing to reject) ?(Choose one - less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to)?(Choose one -12, 45, 38) when, in fact, ? is ?(Choose one - equal to 12, equal to 38, less than 12, less than 38, greater than 38, greater than 45) .

Q2.

A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.2 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, ?, is greater than 7.2 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.7 ounces and that the standard deviation is 0.4 ounces.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making?
	?(Choose one - Type 1, Type 2)
(c)	Suppose the true mean amount of coffee dispensed by the machine is 7.9 ounces. Fill in the blanks to describe a Type II error.
A Type II error would be ?(Choose one - rejecting, failing to reject) the hypothesis that ? is ?(Choose one - less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to) ?(Choose one - 0.4 , 7.7 , 7.2) when, in fact, ? is ?(Choose one - equal to 0.4, equal to 7.2, less than 0.4, less than 7.2, less than 7.7, greater than 7.2 ).

Q3.

A scientist has read that the mean birth weight of babies born at full term is 7.5

pounds. The scientist has good reason to believe that the mean birth weight of babies born at full term, ?, is different from this value and plans to perform a statistical test. She selects a random sample of birth weights of babies born at full term and finds the mean of the sample to be 7.9 pounds and the standard deviation to be 1.5

pounds.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that the scientist decides not to reject the null hypothesis. What sort of error might she be making?
	?(Choose one - Type 1, Type 2 )
(c)	Suppose the true mean birth weight of babies born at full term is 8.1 pounds. Fill in the blanks to describe a Type II error.
A Type II error would be ?(Choose one - rejecting, failing to reject) the hypothesis that ? is ?(Choose one - equal to 7.5, less than or equal to, greater than, greater than or equal to, not equal to, equal to) ?(Choose one - 7.9, 7.5, 1.5) when, in fact, ? is ?(Choose one - equal to 7.9, equal to 7.5, equal to 1.5, not equal to 7.5, less than 1.5, less than 7.9) .

Q4.

The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 110 with a standard deviation of 15.4. The management of the bank suspects that the standard deviation exceeds 15.4. Suppose that the management wants to take a small sample of months and carry out a hypothesis test to see if its suspicions have support. State the null hypothesis H0 and the alternative hypothesis H1 that it would use for this test. H0: I] u 7 P H1: I] An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 690 days and a standard deviation of 120. BIG Corporation claims that the standard deviation of its electric bulbs is less than 120. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test