Regressions

Regressions

100

What is the difference between y & y(hat)

y = actual outcome y(hat) = predicted outcome

200

What is a dependent variable? Which letter signifies a DV? What is an independent variable? Which letter signifies an IV?

Dependent variable = y = variable depends on some other variable Independent variable = x = variable can be used to predict some other variable

300

What is r^2? What can it tell us?

r^2 = coefficient of determination It can tell us what percent of the variation in y can be explained by x

400

For a one tailed test, what changes must you make to your p-value in order to determine whether or not the coefficient is significant?

Must divide p-value by 2 Excel only gives p-value for 2-tailed tests when running regressions

500

In a study of cultural conflicts in multi-national organizations, it is theorized that the main factor that can affect a person’s perception of the intensity of cultural conflicts within the organization is number of years the person spent living/studying overseas. The sample was 100 managers from a multi-national company, and their perception of cultural conflicts within the company was measured on a 10-point scale, with higher scores indicating more perception of cultural conflicts. r^2 = .629 Interpret r-squared

The percentage of variance in perception of cultural conflicts within the company that is predicted by number of years spent studying/living abroad is 62.9%.

Random

100

For a given confidence level and population standard deviation, as sample size increases, what happens to the width of the confidence interval for the sample mean?

It gets narrower

200

If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 - 75(Temperature), what would be the predicted attendance if Temperature is 90 degrees?

9750

300

Late payment of medical claims can add to the cost of health care. A recent study indicated that for one insurance company, 85% of the claims were paid in full when first submitted. Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this system revealed that 180 of the claims were paid in full when first submitted. Was this new payment system effective (alpha = .05)? If the insurance company wants to reduce the probability of making a Type 1 error when testing this hypothesis, then what should be done?

Use a smaller value of alpha (e.g., .01)

400

The fuel economy of a 2009 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is normally distributed with a known standard deviation of 1.25 MPG. If a random sample of 49 tanks of gas yields a mean of 21 MPG, find the 95 percent confidence interval for the true mean MPG.

20.65-21.35

500

Recent EPA fuel economy estimates for automobiles predicted a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume the data is normally distributed. If Cash for Clunkers targeted the 8% of cars with the lowest mpg, what would the cutoff be?

about 16 mpg

Hypothesis Testing

100

For the past two years, the vending machine in the Walton College of Business has charged $1.00 for a bottled soft drink. During this time, company records indicate that an average of μ = 371 soft drinks were sold each week. In September, the company increased the price to $1.25 a can. An analyst randomly samples units sold figures for 8 weeks during the current semester and she finds that after the price increase, units sold per week are as follows: 300, 321, 319, 316, 400, 425, 200, and 221 soft drinks. The standard deviation for these eight weeks is 27 soft drinks and alpha = .05. Dr. Cary Deck, an economics professor, argues that the price increase will result in soft drinks being categorized as a ‘snob good’ by consumers, whereby the increase in price is linked to an increase in demand. On the other hand, common sense suggests that an increase in price will be negatively associated with demand. If you wanted to compare these perspectives (i.e., a price increase results in an increase in demand vs. price increase results in a decrease in demand), what would be the appropriate set of hypotheses?

H 0 : µ = 371 H 1 : µ ≠ 371

200

Healthy Family Medical Center is set up to treat minor medical emergencies for visitors to Myrtle Beach. There are two facilities, one in the River area and one in the Inlet area. Sally, the office manager for both facilities, wants to improve waiting times. She thinks that by streamling patient check-in she can decrease how long patients wait. Sally knows that the patients at both clinics currently wait, on average, about 25 minutes after check-in. In order to test her theory, Sally installs a new check-in procedure at the River area clinic. Patients will send a text message to the office administrator upon arrival. Check in procedures at the Inlet area clinic remained the same as before. At the Inlet area clinic patients, upon arrival, check in at the front desk. To assess this issue, samples of the waiting times for each location (reported in minutes) were recorded. The average waiting time at the River area location was 25.63 minutes with a standard deviation of 5.89 minutes. The average waiting time at the Inlet area location was 25.69 minutes with a standard deviation of 2.68 minutes. What is the appropriate set of hypotheses for this problem?

H 0 : μ River – μ Inlet ≥ 0 H 1 : μ River – μ Inlet < 0

300

Bob, a tenured professor in the College of Business, believes that students’ cumulative GPA increases between their sophomore and senior year. His belief is that as students enter their major, they perform better than when they were taking general education requirements. Bob collects cumulative GPA information for 35 sophomores in the fall of 2010, and then collects cumulative GPA information on the same 35 students when they are seniors in the fall of 2012. Is Bob’s belief correct with a level of significance of .05? What type of test? Hypotheses?

Paired two samples t-Test H 0 : M d(sophomore GPA-Senior GPA) ≥ 0 H 1 : M d(sophomore GPA-Senior GPA) < 0

400

Bob, a tenured professor in the College of Business, believes that students’ cumulative GPA increases between their sophomore and senior year. His belief is that as students enter their major, they perform better than when they were taking general education requirements. Bob collects cumulative GPA information for 35 sophomores in the fall of 2010, and then collects cumulative GPA information on the same 35 students when they are seniors in the fall of 2012. Is Bob’s belief correct with a level of significance of .05? Given that you reject H0, how many of the criteria for inferring causality does this study satisfy?

2

500

An automobile manufacturer is developing a computer for its cars. Among other things, the computer will “talk” to the driver to warn of open doors, unfastened seatbelts, and mechanical problems. The company would like to know whether the computer should speak with a British or American accent, as the chief technology officer of the company believes that the majority of drivers will prefer that the computer speak with an American accent. In a sample of 36 people, 30 preferred the voice with the British accent over the American accent. What hypotheses are being tested? What decision should you make at a 5% level of significance?

H 0 : p≤ .50 H a : p>.50 Fail to reject the null hypothesis; the evidence does not support the chief technology officer’s belief that drivers will prefer the computer speak with an American accent

Old stuff

100

What is the difference between z and t? Under what circumstances would you use each? How do you know if you have a population standard deviation?

Z - population standard deviation or proportions T - sample standard deviation Key words: known, assumed, historic

200

What is Type 1 error? Type 2?

Type 1 = Reject a good H0 Type 2 = Fail to reject a bad H0

300

The incomes of Canadian residents are normally distributed with a mean of $40,000 and a standard deviation of $6,000. What percentage of Canadians have an income between $36k-$46k?

About 59%

400

For Americans, the average number of hours of sleep per night is 7 with a standard deviation of 2.5 hours. A mattress company decides to take a random sample of Americans to review sleeping patterns. Assume normal distributions where needed. What is the probability that a random sample of 25 Americans will have an average of less than 8 hours?

.9772

500

The incomes of Canadian residents are normally distributed with a mean of $40,000 and a standard deviation of $6,000. Above what annual income do the top 1% of all Canadians earn?

$53,980

No Math

100

For the past two years, the vending machine in the Walton College of Business has charged $1.00 for a bottled soft drink. During this time, company records indicate that an average of μ = 371 soft drinks were sold each week. In September, the company increased the price to $1.25 a can. An analyst randomly samples units sold figures for 8 weeks during the current semester and she finds that after the price increase, units sold per week are as follows: 300, 321, 319, 316, 400, 425, 200, and 221 soft drinks. The standard deviation for these eight weeks is 27 soft drinks and alpha = .05. Dr. Cary Deck, an economics professor, argues that the price increase will result in soft drinks being categorized as a ‘snob good’ by consumers, whereby the increase in price is linked to an increase in demand. On the other hand, common sense suggests that an increase in price will be negatively associated with demand. What is the research design of this study?

Non-experimental

200

Healthy Family Medical Center is set up to treat minor medical emergencies for visitors to Myrtle Beach. There are two facilities, one in the River area and one in the Inlet area. Sally, the office manager for both facilities, wants to improve waiting times. She thinks that by streamling patient check-in she can decrease how long patients wait. Sally knows that the patients at both clinics currently wait, on average, about 25 minutes after check-in. In order to test her theory, Sally installs a new check-in procedure at the River area clinic. Patients will send a text message to the office administrator upon arrival. Check in procedures at the Inlet area clinic remained the same as before. At the Inlet area clinic patients, upon arrival, check in at the front desk. To assess this issue, samples of the waiting times for each location (reported in minutes) were recorded. The average waiting time at the River area location was 25.63 minutes with a standard deviation of 5.89 minutes. The average waiting time at the Inlet area location was 25.69 minutes with a standard deviation of 2.68 minutes. What would be the best description of this study?

Quasi-experimental

300

Bob, a tenured professor in the College of Business, believes that students’ cumulative GPA increases between their sophomore and senior year. His belief is that as students enter their major, they perform better than when they were taking general education requirements. Bob collects cumulative GPA information for 35 sophomores in the fall of 2010, and then collects cumulative GPA information on the same 35 students when they are seniors in the fall of 2012. Is Bob’s belief correct with a level of significance of .05? What would a type 1 error be?

Rejecting the null and claiming that cumulative GPA is higher when the student is a senior than a sophomore when in reality it is not true.

400

Bob, a tenured professor in the College of Business, believes that students’ cumulative GPA increases between their sophomore and senior year. His belief is that as students enter their major, they perform better than when they were taking general education requirements. Bob collects cumulative GPA information for 35 sophomores in the fall of 2010, and then collects cumulative GPA information on the same 35 students when they are seniors in the fall of 2012. Is Bob’s belief correct with a level of significance of .05? What would a type 2 error be?

Failing to reject the null and claiming that there is no difference in the cumulative GPA of a senior and sophomore when in reality the cumulative GPA is higher when the student is a senior than a sophomore

500

A variable that could plausibly be causing the results of your study instead of the variable that you had hypothesized as the cause is called the____? How do we get rid of this variable?

Confounding variable True experimental design (random assignment)