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ECO 391

Exam 1 – Fall 2021

1. What is the definition of a mode?

a. The middle value in a distribution

b. The average value of a distribution

c. The most common value in a distribution

d. The dispersion of a distribution

2. Which of the following is a discrete random variable?

a. The distance between two points

b. The amount of time it takes a runner to run a mile

c. The number of students in a class

d. The duration of a solar eclipse

3. A list of test scores for a recent test were 65, 69, 74, 80, 85, 115, and 120. Based on this information is the mean a good measure of the central location.

a. True because the mean is 86 which is within the distribution

b. False because 65 is an outlier to this distribution

c. True because the mean is always a good measure of central location

d. False because 115 and 120 are relatively large and likely outliers.

4. Decide whether the variable is discrete or continuous. The height of a player on a 

basketball team.

a. discrete

b. continuous

5. A recent study found that hamburger fat calories "x" had a positive linear association with the amount of sodium "y" found in that hamburger. This can be interpreted to indicate that:

a. hamburgers with low amount of fat calories have high amount of sodium.

b. low amounts of sodium found in hamburgers indicates a high number of fat calories in the hamburgers.

c. hamburgers with low amount of fat calories tend to have low amount of sodium.

d. high amounts of sodium found in hamburgers causes high amounts of fat calories in hamburgers.

6. The Z-score is:

a. How we get the mean of our sample

b. The value that determines whether our distribution is normal

c. The formula which transforms a normal random variable into a standard normal

d. The number of standard deviations from the mean a sample value is using a normal distribution

7. A sample of test scores was recorded in inches. The distribution of test scores is normal with a mean of 78 points and a standard deviation of 6 points. What is the probability of a test score between 66 and 90 points?

a. 68%

b. 99%

c. 90%

d. 95%

8. A sample of test scores was recorded in inches. The distribution of test scores is normal with a mean of 78 points and a standard deviation of 6 points. What is the probability of scoring over 90%?

a. 97.5%

b. 95%

c. 5%

d. 2.5%

9. A sample of test scores was recorded in inches. The distribution of test scores is normal with a mean of 78 points and a standard deviation of 6 points. What is the approximate probability that you score better than a 96%?

a. 0.1%

b. 1%

c. 99%

d. 0%

10. What is the approximate probability of a Z-value greater than 1.67?

a. 0.0475

b. 0.9525

c. 0.0525

d. 0.3240

11. A frequent hiker tracks the number of steps she takes each day for a month. Assume the number of steps is normally distributed. She finds that she walks an average of 13,500 steps a day with a standard deviation of 3,200 steps a day. What is the probability that she walks between 9,000 and 16,000 steps?

a. 0.703

b. 0.78125

c. 0.9207

d. 0.1384

12. A frequent hiker tracks the number of steps she takes each day for a month. Assume the number of steps is normally distributed She finds that she walks an average of 13,500 steps a day with a standard deviation of 3,200 steps a day. What is the probability that she walks less than 11,000 steps or more than 15,000 steps?

a. 0.2177

b. 0.3192

c. 0.5369

d. 0.1015

13. A frequent hiker tracks the number of steps she takes each day for a month. Assume the number of steps is normally distributed. She finds that she walks an average of 13,500 steps a day with a standard deviation of 3,200 steps a day. What is the probability that she walks more than 13,500 steps?

a. 50%

b. 45%

c. 67%

d. 54%

14. A frequent hiker tracks the number of steps she takes each day for a month. Assume the number of steps is normally distributed. She finds that she walks an average of 13,500 steps a day with a standard deviation of 3,200 steps a day. What is the probability that she walks less than 9,500 steps?

a. 0.05125

b. 0.1056

c. 0.1346

d. 0.1672

15. The value of the _____ is used to estimate the value of the population parameter.

a. sample statistic

b. sample parameter

c. population statistic

d. population estimate

16. As the sample size increases, the:

a. standard error of the mean increases.

b. population mean increases.

c. standard deviation of the population decreases.

d. standard error of the mean decreases.

17. A food tester wants to test the spice level of a Carolina Reaper pepper. They know that the average Scoville level of a Carolina Reaper is 2 million Scoville. They want to test the probability of a particular pepper being more than 2.2 million Scoville. The food tester is performing a:

a. Right tailed test

b. Left tailed test

c. Two tailed tests

d. No tailed test

18. The number of tips at a local restaurant has a mean of $50 per server per night and 72% of nights each server makes more than $50 a night. Is the number of tips at this restaurant normally distributed?

a. Yes, because it has a mean and standard deviation

b. No because more than half the probability is greater than the mean

c. No because the standard deviation would be too high to be normal

d. We need more information to determine.

19. As the test statistic becomes larger, the p-value:

a. becomes larger.

b. becomes smaller.

c. stays the same, since the sample size has not been changed.

d. becomes negative.

20. Which of the following null hypotheses cannot be correct?

a. 

b. 

c. 

d. 

21. Which of the following is not a characteristic of a normal distribution?

a. The distribution is symmetric

b. It has a mean of 1

c. The mean is equal to the median

d. The distribution is bell shaped

22. What is the median of a normal distribution with mean 6?

a. 6

b. 12

c. 3

d. 4

23. Which of the following represents a population and a sample of that population?

a. Customers of a bank as the population, and customers of all the banks in the area as the sample

b. Chickens at a farm are the population, and cows at the farm are the sample

c. Chocolates in a box of chocolates is the population, and the number of vanillas filled chocolates is the sample

d. The classes offered at the university is the population, and the students in a class is the sample.

24. A teacher randomly chooses students’ names out of a hat to determine who she will ask a question to. All students have an equal likelihood of having their name pulled out of the hat. What kind of sampling is this?

a. Simple random sampling

b. Cluster sampling

c. Convenience sampling

d. Stratified random sample

25. As each employee enters the office one day at work, their boss draws a card. When the ace of spades is drawn, that employee and every third employee after is questioned about their satisfaction with the workplace. What sort of random sampling is this?

a. Cluster sampling

b. Convenience sampling

c. Systemic sampling

d. Simple random sampling

26. A restaurant asks the first 20 people to enter the restaurant one day to provide feedback on their dining experience. What sort does this represent?

a. Cluster sampling

b. Convenience sampling

c. Stratified random sampling

d. Systemic sampling

27. The alternative hypothesis is:

a. The statement we want to prove

b. The statement we believe applies to the population

c. Any statement we know is true

d. None of these options

28. If we find insufficient evidence to suggest that the alternative hypothesis is true then we:

a. Reject the null hypothesis

b. Accept the null hypothesis

c. Fail to reject the null hypothesis

d. Reject the alternative hypothesis.

29. A professor wants to test if this year’s test scores is significantly different from previous years test scores. In previous years, the average score on the exams was 80 points. What is the set of hypotheses for this test?

a. 

b. 

c. 

d. 

30. Stratified random sampling is a method of selecting a sample in which _____.

      a. the sample is first divided into groups, and then random samples are taken from each

                    group

      b. various strata are selected from the sample

      c. the population is first divided into groups, and then random samples are drawn

                    from each group

      d. None of the answers is correct.

31. A restaurant wants to test how many orders they get wrong on average a night. They believe that they normally mess up 14 orders with a standard deviation of 3 orders. What is the variable of interest?

a. The number of orders a night

b. The number of take out orders messed up a night

c. The number of diners at the restaurant a night

d. The number of orders the restaurant messes up a night

32. Consider the following student’s process for completing a significance test. They first determine the variable of interest and conjectures an alternative hypothesis. They write down a set of hypotheses using their variable of interest. Finally, they test the significance of their findings assuming their alternative hypothesis is true. What mistake did they make in this process?

a. They should have conjectured a null rather than an alternative hypothesis

b. They should have tested the significance of their findings before writing down their hypotheses

c. They should have not chosen a single variable of interest

d. They should not have assumed that their alternative hypothesis was true

33. A professor wants to determine if the scores on the first exam in a semester were significantly improved from previous semesters. The first exam in the past had normally distributed grades with an average score of 76 with a standard deviation of 9. On the second exam the average score for 36 students on the exam was a 87. What is the test statistic?

a. 7.33

b. 6.45

c. 4.44

d. 5.23

34. We want to conduct a test on whether the amount of poison in a person’s body significantly greater than zero. We find a p-value of 0.03 and the mean value is greater than zero. Does this evidence indicate at the 95% confidence level that there is poison in the person’s body?

a. Yes, because the p-value is smaller than .05

b. No, because the p-value is greater than .05

c. No, because the mean value is greater than zero

d. Yes, because the mean value we found was greater than zero

35. In Ordinary Least Squares regressions we:

a. Create a regression line which minimizes SSE

b. Create a regression line that maximizes the dependent variable

c. Create a regression line to touch all the observations

d. Create a regression line that maximizes the SSE

36. What is a residual?

a. The value of the dependent variable for a given set of independent variable values.

b. The difference between out observed Y-value and the estimated Y-value

c. The difference between the various observed Y-values

d. The ratio of explained variation in Y to unexplained variation in Y

37. A radar unit is used to measure speeds of cars on a highway. The speeds are normally distributed with a mean of 70 mph and a standard deviation of 5 mph. What is the approximate probability that a car picked at random is travelling at more than 80 mph?

0.95

0.975

0.05

0.025

38. A weather forecaster wants to estimate rainfall during October using humidity, amount of rainfall in September, and temperature. What is the dependent variable of this model?

a. Temperature

b. Rainfall previous month

c. Humidity

d. Rainfall in October

39. A worker records their income for the first 6 months of a year to try to estimate their income in the second half based on the number of hours they work. They got the following result.

Months	January	February	March	April	May	June
Income	$40,100	$37,375	$42,650	$48,000	$35,500	$50,250
Hours worked	120	109	131	153	98	162

What is the relationship between hours worked and income?

a. Negative

b. No relationship

c. Positive

d. Needs more information

40. The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the values of ɛ are:

a. limited.

b. uniformly distributed.

c. independent.

d. categorical.

41. The estimated regression equation, , can be used to predict a company's sales volume (y), in millions, based upon its advertising expenditure (x), in $10,000s. What is the company's predicted sales volume if they spend $500,000 on advertising?

a. Approximately $50 million

b. Approximately $29 million

c. Approximately –$6.5 million

d. Approximately $395,000

42. Following is a portion of the computer output for a regression analysis relating Y = number of people who use the public pool to X = the outside temperature in degrees Celsius.

 

Interpret the coefficient for temperature.

a. All else equal, on average a 1 degree increase in the outside temperature would lead us to predict a 0.811 person increase in the number of people at the pool.

b. A 1 degree increase in the outside temperature will increase the number of people at the pool by 0.811

c. All else equal, on average a 1 degree increase in the outside temperature would lead us to predict a 0.811 person decrease in the number of people at the pool.

d. A 1 degree increase in the outside temperature will decrease the number of people at the pool by 0.811