0.+Exam+1+-+ECO+391+-+Fall+2022+%28Q%26A%29+42+questions+UPLOADED

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

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

24. The manufacturing process for a 30 pound dumbbell is slightly imprecise, so the actual weight follows a normal distribution with a mean of 30 pounds and a standard deviation of 0.01 pounds. At the end of the process, a sensitive scale is used, and all dumbbells that are more than 0.02 pounds away from 30 are not sold at full price. What percent of dumbbells are not sold at full price? a. 50 b. 32 c. 5 d. 1 25. Systolic blood pressure in healthy adults has a normal distribution with mean 112 mmHg and standard deviation 10 mmHg. What percentage of adults will have blood pressure above 122mmHg? a. 16 b. 50 c. 68 d. 0.3 26. The radar gun model used by a police department to measure the speed of cars has a measurement error that follows a normal distribution with mean of 0 mph and standard deviation of 1.5 mph. Approximately what percent of readings will overestimate the speed of a car by more than 5mph? a. 0 b. 16 c. 68 d. 50 27. Using the standard normal distribution, what is the probability that z < 1.5? a. 0.50 b. 0.69 c. 0.93 d. 0.98 28. Using the standard normal distribution, what is the probability that z is between 0 and 1.1? a. 0.36 b. 0.44 c. 0.86 d. 0.22

29. Using the standard normal distribution, what is the probability that z < - 0.5? a. 0.22 b. 0.29 c. 0.31 d. 0.39 30. A researcher has a dataset that contains information on the weight of a variety of types of fish and possible determinants of weight. She runs a simple regression using weight in grams as the dependent variable and length in cm as the independent variable, and obtains the results below. Coefficients Standard Error t Stat P-value Intercept -488.581565 31.14187781 -15.68889 5.734E-34 Length cm 28.45831278 0.935112133 30.433048 9.801E-68 An increase in length of 1cm is associated with how many grams of increase in weight? a. 31.14 b. 0.94 c. 30.43 d. 28.46 31. A researcher has a dataset that contains information on the weight of a variety of types of fish and possible determinants of weight. She runs a simple regression using weight in grams as the dependent variable and length in cm as the independent variable, and obtains the results below. Coefficients Standard Error t Stat P-value Intercept -488.581565 31.14187781 -15.68889 5.734E-34 Length cm 28.45831278 0.935112133 30.433048 9.801E-68 Which of the following is the sample regression equation? a. Weight = -488 + 31*length b. Length = -488 + 31*weight c. Weight = -488 + 28*length d. Length = -488 + 28*weight

37. A researcher collects a dataset that has the ACT and SAT scores for a sample of students who took both tests. She is interested in the relationship between scores for individuals. Which of the following values is she most interested in? a. Correlation coefficient between ACT and SAT score b. Standard deviations of ACT and SAT scores c. Mean ACT and SAT score d. Variance 38. The table below shows the final grade distribution for a statistics class. What is the median letter grade? Grade Percent of Class A 30% B 40% C 10% D 5% E 15% a. A b. B c. C d. E 39. A population is normally distributed with a mean of 5,398 and standard deviation of 6.71. A researcher collects a sample of 1,698 observations. Approximately, what is the variance in the population? a. 11 b. 45 c. 112 d. 209 40. As a general guideline, the research hypothesis should be stated as the _____. a. null hypothesis b. alternative hypothesis c. tentative assumption d. hypothesis the researcher wants to disprove

41. A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ^ y = 50,000 + 6*X The above equation implies that an increase of _____. a. $6 in advertising is associated with an increase of $6,000 in sales b. $1 in advertising is associated with an increase of $6 in sales c. $1 in advertising is associated with an increase of $56,000 in sales d. $1 in advertising is associated with an increase of $6,000 in sales 42. Assume z is a standard normal random variable. Then P (–1.20 ≤ z ≤ 1.50) equals _____. a. 0.0483 b. 0.3849 c. 0.4332 d. 0.8181 AUTHORIZED FORMULAS:

The z-table (Left tail test)

ANSWER KEY 1. Solution: A. The mode is the observation that occurs most frequently in a dataset. Here, zero occurs twice, while all other values occur only once. 2. Solution: C. Outliers may cause the mean to far away from the median. 3. Solution: C. If there are an odd number of values in a data set, the median is the value that is in the middle when the values are listed in order. If there are an even number of values in a data set, the median is the average of the middle two values. In this case, the median itself may not be a value in the data set. 4. Solution: B . Multiply each of her grades by the corresponding percentage from the chart (converted to decimal form). Sum these numbers. 5. Solution: C . A sample will be cheaper than a census. A potential weakness of simple random sampling is that the sample may not be representative. 6. Solution: C . If a population is separated into groups and then only certain groups are selected for study (with every member of the group studied), then it is cluster sampling. 7. Solution: B. If a population is separated into groups based on certain traits (in this case age and gender) and then a sample is drawn from each group, it is stratified random sampling 8. Solution: D. If a sample is drawn that is different from the population under consideration, and this difference causes conclusion to be biased, we have selection bias 9. Solution: C . If every member of a population is studied rather than just a sample, we have a census. 10. Solution: D . Convenience sampling is when a sample is drawn based on convenience, such as only speaking to people on the street outside of your office. 11. Solution: A . The null hypothesis must include the equal sign, the greater than or equal to sign, or the less than or equal to sign. Only choice A meets this criterion. Usually, if the researcher wants to test whether some hypothesis is true, then that hypothesis is the alternative, and all other possibilities fall under the null. 12. Solution: C. She wants to determine whether the mean pH is greater than 7, so that is the alternative hypothesis. 13. Solution: D . If the alternative hypothesis is μ > some number, then we have a right- tailed test. 14. Solution: D . The z-score formula is z =( x − μ )/( σ / √ n ) . We can plug in to get ( 0.3 − 1.5 )/( 2.9 / √ 250 ) = -6.54 15. Solution: A . The z score is 4.9 − 6 3 √ 144 =− 4.4 . 16. Solution: A . At the 10% level, we should reject the null if the p-value < 0.10. 17. Solution: D. The possibility that the researcher is interested in is the alternative hypothesis. 18. Solution: A. If a researcher can reject the null at the one percent level, she can certainly reject it at the five or ten percent levels, because the rejection region will be larger. 19. Solution: D . Apply the z formula: ( 37 − 30 )/( 8 / √ 50 )= 6.19 20. Solution: B . We can count the number of televisions in a home, so it is discrete. The other values cannot be counted, but can be measured to any degree of accuracy, so they are continuous, not discrete.

39. Solution: B. The population variance is always the square of the population standard deviation. Take 6.71 and square it to obtain the answer. Most of the information in this question is not necessary to obtain the solution. 40. Solution: B. The null hypothesis refers to the default state of nature. The alternative hypothesis typically contests the status quo, for which a corrective action may be required. 41. Solution: D. As x increases by 1 unit, y is expected to change by the amount of the slope coefficient. Since the slope is 6, when advertising increases by one dollar, sales are expected to increase by $6,000 (y is in $1000). 42. Solution: D. P (–1.20 ≤ z ≤ 1.50) = P(z ≤ 1.50) - P(z ≤ -1.20) = 0.9332 – 0.1151 = 0.8181 COMPOSITION OF THE EXAM : Chapter 03: 08 questions Chapter 06: 11 questions Chapter 07: 06 questions Chapter 09: 08 questions Chapter 12: 02 questions Chapter 14 : 07 questions Total 42 questions