# Mathematics

Finite Math 130 Final Exam Spring 2015 Central Washington University

June 1, 2015

Name_____________________________/

Instructions: This is an open book, open note final exam. Please work all 10 problems. The exam is due June 8, 2015 by noon. Write your exam on notebook paper (do not write your answers on the question sheet) and staple the question sheet to the front of the exam when you are done. Show your work to receive credit for the exam (not just the final answer but the calculations).

Sampling

1) Describe how to select a simple random sample from a population.

2) Describe how to select a systematic sample from a population.

3) Describe how to select a cluster sample from a population.

Confidence Intervals

4) A random sample of customer order totals with an average of $78.25 and a population standard deviation of $22.50. Calculate a 90% confidence interval fro the mean, given a sample size of 75 orders.

5) A random sample of 35 teenagers averaged 7.3 hours of sleep per night. Assume the population standard deviation is 1.8 hours. Calculate a 98% confidence interval for the mean.

6) Below is the data set for the amount of trash by ten households (in pounds per day). Assume the population is normally distributed.

Pounds of trash

3.9 4.6 15.6 10.5 16.0 6.7 12.0 9.2 13.8 16.8

Construct a 95% confidence interval for the mean based on the sample. Calculate the sample mean. Hint: use the t-table.

Hypothesis Testing for a Single Population

8) A company claims the average time a customer waits on hold is less than 5 min. A sample of 35 customers has an average wait time of 4.78 min. Assume the population standard deviation for wait

time is 1.8 min. Test the company claim at the α = 0.05 significance level by comparing the calculated

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z-score to the critical z-score.

9) We are testing the claim that houses in a particular community average less that 90 days on the market. A random sample of 9 homes averaged 77.4 days on the market with a sample standard

deviation of 29.6 days. Assume the population is normally distributed. Test the claim at the α = 0.05 significance level by comparing the calculated t-score to the critical t-score.

Decision Theory

10) B.F. Retread, a tire manufacturer, wants to select one of three feasible prototype designs for a new tire; A, B, C.

Sales Event

Demand Low Medium High

Probability .30 .50 .20

A 120,000 255,000 390,000

B 130,000 295,000 460,000

C 100,000 300,000 480,000

1) What is the best optimistic decision? 2) What is the the best pessimist solution? 3) What is the best avoidance of regret solution?

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- Probability