What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?

Suppose that the average price for a gallon of gasoline in the United States is $3.73 and in Russia is $3.40. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the United States and a standard deviation of $.20 in Russia.

a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?

b. What percentage of the gas stations in Russia charge less than $3.50 per gallon?

c. If current average price for a gallon of gasoline in the United States is $3.63 with a standard deviation of $0.25. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 4 – 10 pts

Assume the population standard deviation is σ = 25.

a. Compute the σx̄, for sample sizes of 50, 100, 150, and 200. (5 pts)

b. What can you say about the σx̄ as the sample size is increased? (5 pts)

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 5 – 10 pts

Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486. Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is σ = $650.

a. Develop a 90% confidence interval estimate of the population mean monthly rent. (5 pts)

b. Develop a 95% confidence interval estimate of the population mean monthly rent. (5 pts)

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 6 – 10 pts

Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.

a. Develop the null and alternative hypotheses most appropriate for this study.

b. Comment on the conclusion when H0 cannot be rejected.

c. Comment on the conclusion when H0 can be rejected.

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 7 – 10 pts

Consider the following hypothesis test: H0 : µ ≥ 80 vs Ha : µ < 80. A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

a. x̄ = 78.5 (5 pts)

b. x̄ = 81 (5 pts)

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 8 – 10 pts

Consider the following hypothesis test: H0 : µ = 22 vs Ha : µ ̸= 22. A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

a. x̄ = 23 (3 pts)

b. x̄ = 25.1 (4 pts)

c. x̄ = 20 (3 pts)

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 9 – 10 pts

Consider the following hypothesis test: H0 : µ ≥ 45 vs Ha : µ < 45 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

a. x̄ = 44 and s = 5.2 (4 pts)

b. x̄ = 43 and s = 4.6 (3 pts)

c. x̄ = 46 and s = 5.0 (3 pts)

CRN 19915 Name: Final Exam

MGMT 5311 Z01

Problem 10 – 10 pts

Consider the following hypothesis test. H0 : µ1 − µ2 ≤ 0 vs Ha : µ1 − µ2 > 0.

Sample 1 Sample 2 n1 = 40 n2 = 50 x̄1 = 25.2 x̄2 = 22.8 σ1 = 5.2 σ2 = 6.0

The following results are for two independent samples taken from the two populations.

a. What is the point estimate of the difference between the two population means?

b. What is the value of the test statistic?

c. What is the p-value ?

d. With α = 0.05, what is your hypothesis testing conclusion?