This Is a Sample Practice Exam Based on Concepts That Will Be Covered on the Actual Exam

Leader: Ben Introduction to Statistics Course: STAT 226 Supplemental Instruction Instructor: Dr. Genschel Iowa State University Date: THIS IS A SAMPLE PRACTICE EXAM BASED ON CONCEPTS THAT WILL BE COVERED ON THE ACTUAL EXAM. IN NO WAY SHOULD THIS PRACTICE EXAM BE TREATED AS A REALISTIC REPRESENTATION OF THE ACTUAL STAT 226 EXAMINATION

1. True/False a. The mean of the t-distribution is at 0

b. A 99% confidence interval can be interpreted as 99% of all ISU students are between 5 feet and 5’12’’.

c. If a population distribution is skewed, a sample size of 15 is sufficient for the sampling distribution to be approximately normal.

2. What is a sample distribution?

3. Political polls have the potential to be biased. How can a researcher reduce the risk of bias when collecting sample data?

4. ABC Technology researchers were excited to announce that they have come up with a new process improvement. In the old process a machine was able to make 100 records a minute. A random sample of 30 days showed that the average number of records made a minute was 102 records with a standard deviation of 6 records. Does the new production process appear to be more efficient than the old process?

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu 5. A lumber mill creates numerous wood planks from oak trees, pine trees, and maple trees. A plank creating machine makes 6 feet planks. The lumber mill’s customers are very specific in that they want planks that are exactly 6 feet. The customers randomly sample 50 wood planks and find the mean length to be 6.1 feet with a standard deviation of 0.2 feet. Does it appear that there is an issue with the plank production process?

6. One of your friends recently went on a Minnesota Fishing Trip. He claims that the average length of Northern Pike he caught was 36 inches. Skeptical of these claims, you randomly select 20 Northern Pike from the same lake and find the average length was 35 inches with a standard deviation of 8 inches. Do you have statistical evidence to suggest your friend exaggerated (people tend not to underestimate fish length)? 7. A 90% confidence interval is as follows: (65, 75). The population standard deviation is known and the sample size is 30.

What is the sample mean?

What is the population standard deviation?

8. A researcher is interested in determining the average tusk length of elephants in Namibia. The population standard deviation is unknown. She randomly selects 40 elephants and finds that the mean is 38 inches and the standard deviation is 6 inches. What is the 95% confidence interval for the tusk length?

9. A statistics student is interested in estimating the mean height of all statistics students. The standard deviation of all statistics students is equal to 0.5 feet. A random sample of 81 students had mean height of 5.8 feet. What is the 90% confidence interval?

10. The census bureau is interested in knowing the average income for the United States. The sampling distribution is as follows x ~ N(40,000, 9,000) for a sample size of 100. What is the z-score of achieving a sample mean greater than $54,000 for a sample size of 100? 11. A random sample of 80 dogs yielded an average weight of 41 pounds and a standard deviation of 6 pounds. Is there evidence to suggest that the average weight of all dogs is less than 42 pounds?

12. Volkswagen advertises that its new sedan gets better than average gas mileage. The average gas mileage for cars in the United States is 23.6 miles per gallon. After randomly sampling 60 Volkswagen cars, the average miles per gallon is 25.2 miles per gallon with a sample standard deviation of 3 miles per gallon. Does it appear that Volkswagens claims are reasonable?

13. A researcher is interested in studying tree height. A sampling distribution for size 50 is as follows x ~ N(16,2). What is the probability for observing a sample mean greater than 15.5 for a sample size of 50 trees?