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Last Name: ____________________ First Name: ____________________ ECO 391 (Fall 2022) Exam 1 Directions: ● You have 60 minutes to complete the exam and it is out of 100 points. ● Multiple choice 1 to 42 are worth 2.38 points per question. Good Luck!!!

1. A sample of seven recent college graduates shows how much college debt each student carries. The numbers are $0, $9,842, $11,005, $15,803, $0, $27,209, and $98,001. What is the mode? a. 0 b. 11,305 c. 25,553 d. 27,209 2. Arthur calculates the mean and the median for a data set, and finds that they are far apart. What might be the reason for this? a. The standard deviation is very low b. The data follow a normal distribution c. The data have outliers d. There is no mode in the data 3. At the end of the semester, the median grade in a statistics class is equal to 81, yet no student in the class had a final grade of 81. Which of the following must be true? a. The data contain outliers b. There are multiple modes c. There is an even number of students in the class d. The grades have a high variance 4. The graph below shows the weighting of assignments of Alice’s History Course. Assignment Weight Class Participation 10% Midterm 20% Final Paper 20% Final Exam 50% Her final grade will be out of 100. She made a 100 for class participation, an 80 on the midterm, a 90 on the final paper, and a 96 on the final exam. What is her final grade in the class? a. 85 b. 92 c. 95 d. 96

5. The Nielsen company collects a Simple Random Sample of residents in Lexington and has each member take a survey about their local shopping habits (no one refuses to fill out the survey). What is a potential weakness of this sampling strategy? a. The sample may be biased b. A lot of demographic information must be known about the population prior to sampling c. The sample may not be representative d. It is probably expensive relative to taking census of the population of Lexington 6. Every member of the Freshman class at a university has to take a freshman seminar in the Fall semester. Everyone is in a seminar and no one is in more than one seminar. The university randomly selects a subset of these seminars, and then surveys every student in those classes. Which type of sampling method is being used? a. Simple random b. Stratified random c. Cluster d. Systematic 7. The Nielsen media company wants to estimate how many viewers watched the Super Bowl. They divide the population into 3 categories by age, and then divide each category by gender, adding up to 6 categories total. They then randomly select a sample from each category. Which type of sampling method is being used? a. Simple random b. Stratified random c. Cluster d. Systematic 8. In the 1960 presidential debate between John F. Kennedy and Richard Nixon, a sample of individuals who watched the debate on television indicated that the number of viewers who believed Kennedy won the debate was much larger than the number who believed that Nixon won. This evidence has been used to support the idea that Kennedy’s debate performance helped him win the election. It has been argued that this evidence is problematic because young people were more likely to already support Kennedy, and they were also more likely to watch the debate on TV, whereas older people were more likely to support Nixon but also more likely to listen to the debate on the radio. If this critique is true, the sample of tv viewers suffers from which problem? a. Non-response bias b. Cluster error c. Systematic error d. Selection bias

9. The University of Kentucky attempts to collect answers to three questions about Covid- 19 from every member of the student body in order to draw conclusions about the student body. What are they carrying out? a. Cluster sample b. Systematic sample c. Census d. Stratified random sample 10. A local TV station has an office in downtown Louisville. To gauge opinion on a mayoral race, they set up a camera on the sidewalk outside of the office and interview several passersby. Which of the following methods are they using? a. Systematic sampling b. Simple random sampling c. Cluster sampling d. Convenience sampling 11. Previous research indicates that the mean household in the United States owns 1.8 cars. A researcher collects a sample to test whether the mean is different from this number. What should be the null hypothesis? a. μ = 1.8 b. μ≠ 1.8 c. μ < 1.8 d. μ > 1.8 12. An environmental scientist collects a sample of 10 pH readings from a large pond. She wants to determine whether the mean pH is greater than 7. What should be the alternative hypothesis? a. The sample mean is greater than 7 b. The sample mean is less than or equal to 7 c. The population mean is greater than 7 d. The population mean is less than or equal to 7 13. If the alternative hypothesis is μ > 0 , what type of test is being performed? a. Two-tail b. Three-tail c. Left-tail d. Right-tail

14. Historical trends show that the average renter in Fayette county pays rent 1.5 days early. An economist collects a sample of 250 renters in Fayette in order to test whether this number was lower than 1.5 for the month of July 2020. The sample mean is 0.3, and the population standard deviation is assumed to be 2.9. What is the test statistic (z score)? a. 3.98 b. -4.67 c. 5.08 d. -6.54 15. Acer claims that one of its laptop models lasts 6 years on average. A researcher collects data on 144 laptops and finds a sample mean of 4.9 years. Assume the standard deviation is 3 years. What is the relevant test statistic (z score)? a. -4.4 b. -5.9 c. -7.2 d. -8.7 16. Lenovo claims that one of its laptop models lasts 5 years on average. A researcher conducts a hypothesis test at the 10% level with the null hypothesis that this statement is true. The p-value is 0.01. Does the researcher reject the null hypothesis? a. Yes b. No 17. A researcher is interested in determining whether the mean of a population is greater than 10. What should be the alternative hypothesis? a. μ≤ 10 b. μ≥ 10 c. μ ≼ 10 d. μ ≻ 10 18. A researcher surveys a group of respondents to determine the average amount of time spent in a car per day. She tests the hypothesis that this amount of time is larger than 30 minutes and rejects the null hypothesis at the 1% level. Which of the following is true? a. She can certainly reject the null hypothesis at the 5% level b. She can possibly reject the null hypothesis at the 5% level, but possibly cannot c. She can certainly not reject the null hypothesis at the 5% level d. She can certainly not reject the null hypothesis at the 10% level

19. A researcher wants to test the hypothesis that the average number of miles that a 2010 Honda Civic can drive after its gas meter reads as empty is greater than 30. She collects data from a sample of 50 cars and finds a sample mean of 37. She assumes the standard deviation is 8 based on a literature about car manufacturing. What is the test statistic? a. 1.99 b. 2.86 c. 4.55 d. 6.19 20. Which of the following variables is discrete? a. Finishing times for a 100 meter race b. Number of televisions in a household c. Head circumference of infants d. Volume of soda cans 21. Which of the following is not a property of the normal distribution? a. The mean, median and mode are all equal b. The tails asymptotically approach the horizontal axis c. The area underneath the curve and to the right of the mean is 1 d. It has a bell shape 22. X is a random variable that is normally distributed with a mean of 0 and standard deviation of 10. If X = 20, what is the corresponding z-score? a. 1.96 b. 2 c. 3.39 d. 3.88 23. A standardized test has scores that are normally distributed with a mean of 120 and a standard deviation of 20. Anastasia scores a 110. What is the z-score corresponding to her test score? a. -2 b. -0.5 c. 0.5 d. 2

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