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Hypothesis testing (technically also old stuff)
More hypothesis testing
(technically also old stuff)
Regressions
100
Student records indicate that the population of students at Uber University consumes foods and beverages containing an average of 150 mg of caffeine per day. The standard deviation for caffeine consumption among all students is known to be 15 mg per day. You talk to Emily, a student at Uber University, and learn that she consumes 135 mg of caffeine per day. If you randomly select another student, what is the probability that he or she consumes less caffeine than Emily?
.16
100
Assume that Sarah has no information about the caffeine consumption at Uber University. She coordinates a meeting of students to discuss consumption of caffeine. At the meeting, she surveys the 49 students and finds, for these 49 students, the mean daily caffeine consumption is normally distributed with a mean of 154 and a standard deviation of 12 mg. Does the true population mean (150 mg) fall within a 90 percent confidence interval (calculated based on this sample)?
No
100
The average diastolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment banking jobs. Heart attack is the leading cause of death in the US, and the American Medical Association (AMA) deems average systolic blood pressure of 140 mm as very high. The fitness instructors and AMA doctors recommend practicing Yoga. They believe that practicing yoga reduces blood pressure and hence is beneficial to people. To test this claim, a sample of 51 investment bankers who had previously been diagnosed with high blood pressure was chosen. Participants were trained and completed yoga exercises for six months. At the end of the six months, the average blood pressure for the sample was 139 mm with a standard deviation of 5 mm. What type of test? What would be the proper set of hypotheses?
One sample t-test H0: μ = 140, H1: μ < 140
100
In recent years, a number of web-based head hunting firms (i.e., companies that offer job placement services) have been created. Suzy Matchmaker, the owner of one such company, wanted to investigate the job offers that recent business majors were obtaining. In particular, Suzy believes that accounting majors were being offered higher salaries than management majors. To test this belief, Suzy began by examining transcripts of accounting and management majors. She then randomly selected an accounting and a management major whose grade point average (GPA) falls between 3.92 and 4 (the GPA scale had a maximum value of 4). She then randomly selected an accounting and a management major whose GPA is between 3.84 and 3.92. She continued this process until the 25 th pair of accounting and management majors is selected whose GPA fell between 2.0 and 2.08 (the minimum GPA required to graduate is 2.0). From each participant, Suzy obtained the highest salary offer. Assume α = .10 for this scenario. What type of test is this? What are the hypotheses?
Matched Pairs T-test Ho: Md (accounting - management) ≤ 0 Ha: Md (accounting - management) > 0
100
In recent years, a number of web-based head hunting firms (i.e., companies that offer job placement services) have been created. Suzy Matchmaker, the owner of one such company, wanted to investigate the job offers that recent business majors were obtaining. In particular, Suzy believes that accounting majors were being offered higher salaries than management majors. To test this belief, Suzy began by examining transcripts of accounting and management majors. She then randomly selected an accounting and a management major whose grade point average (GPA) falls between 3.92 and 4 (the GPA scale had a maximum value of 4). She then randomly selected an accounting and a management major whose GPA is between 3.84 and 3.92. She continued this process until the 25 th pair of accounting and management majors is selected whose GPA fell between 2.0 and 2.08 (the minimum GPA required to graduate is 2.0). From each participant, Suzy obtained the highest salary offer. Assume α = .10 for this scenario. What is the dependent variable in this scenario?
Salary offer
200
Student records indicate that the population of students at Uber University consumes foods and beverages containing an average of 150 mg of caffeine per day. The standard deviation for caffeine consumption among all students is known to be 15 mg per day. Your roommate tells you that his caffeine consumption is 1.3 standard deviations above the mean. About how many mg of caffeine does your roommate consume each day?
170mg
200
Student records indicate that the population of students at Uber University consumes foods and beverages containing an average of 150 mg of caffeine per day. The standard deviation for caffeine consumption among all students is known to be 15 mg per day. You randomly select 42 students from Uber University to complete a survey on caffeine consumption and find average daily consumption to be 145 mg. Assuming that the sample of students is from a normal population, what is the 80% confidence interval for the true population mean?
142, 148 mg
200
The average diastolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment banking jobs. Heart attack is the leading cause of death in the US, and the American Medical Association (AMA) deems average systolic blood pressure of 140 mm as very high. The fitness instructors and AMA doctors recommend practicing Yoga. They believe that practicing yoga reduces blood pressure and hence is beneficial to people. To test this claim, a sample of 51 investment bankers who had previously been diagnosed with high blood pressure was chosen. Participants were trained and completed yoga exercises for six months. At the end of the six months, the average blood pressure for the sample was 139 mm with a standard deviation of 5 mm. What is the value of the test statistic?
t=-1.43
200
Considering the risk involved in actually deploying the “Submit Your Contact Details” form on potential sales, Rodrigo suggests working with the Walton College Behavioral Lab to examine the effects of such changes on consumer download behavior. Accordingly, Nancy seeks the help of her professor, Dr. Burton. Dr. Burton recommends creating two websites – one with no form and another with the contact details form, and randomly assigning people to one of the two conditions. If a customer (participant in the study) downloads the software, it is recorded as 1. If the customer does not download the software, it is recorded as 0. Which test should Nancy perform if she followed Dr. Burton’s recommendation ? What type of experimental design?
Z-test two sample proportions True experimental design
200
Brooke recently graduated from the Sam Walton College of Business and moved to New York City to accept a job on Wall Street as a financial analyst. Her supervisor requested that she analyze 30 stocks within the healthcare industry and wanted her to predict stock price based on cash, income, and inventory levels. The analyst produced the following output using α = .05. What set of hypotheses is the analyst trying to test for the model?
H 0 : B income = B inventory = B cash = 0, H 1 : At least one B =/= 0
300
Starbucks is interested in decreasing customer wait times. They think that training employees according to a new set of procedures will decrease waiting times. To test the usefulness of the training, they pick two locations and have all employees at one location trained. Employees at the other location do not receive the training. They measure wait times for both locations one week after the training. What kind of research design does this represent?
Quasi-experimental
300
The New Life Insurance Company has recently restructured jobs in their claims processing division. A main goal of the change was to decrease the amount of time to process claims. Prior to the restructure, claims took an average of 14.5 work days to process. To test the effectiveness of the new job structure, the division manager collected a random sample of 100 claims 6 months after the restructure and found that they took an average of 12.7 work days to process, with a standard deviation of 2.2 days. What type of statistical test should she perform?
One sample t-test
300
The average diastolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment banking jobs. Heart attack is the leading cause of death in the US, and the American Medical Association (AMA) deems average systolic blood pressure of 140 mm as very high. The fitness instructors and AMA doctors recommend practicing Yoga. They believe that practicing yoga reduces blood pressure and hence is beneficial to people. To test this claim, a sample of 51 investment bankers who had previously been diagnosed with high blood pressure was chosen. Participants were trained and completed yoga exercises for six months. At the end of the six months, the average blood pressure for the sample was 139 mm with a standard deviation of 5 mm. What is the correct decision (assuming α = .025)? What are we saying?
Fail to reject the null Learning Yoga is not useful to people with high responsibility jobs who have high blood pressure.
300
According to an online survey by Harris Interactive for the job site CareerBuilder.com, more than half of IT workers say they have fallen asleep at work. Sixty-four percent of government workers admitted to falling asleep on the job. Do more government workers admit to falling asleep on the job than IT workers? What type of test? Hypotheses?
z test - 2 sample proportions H 0 : P it - gov ≥ 0, H 1 : P it - gov < 0
300
Brooke recently graduated from the Sam Walton College of Business and moved to New York City to accept a job on Wall Street as a financial analyst. Her supervisor requested that she analyze 30 stocks within the healthcare industry and wanted her to predict stock price based on cash, income, and inventory levels. The analyst produced the following output using α = .05. Regression Statistics Multiple R 0.8714 R Square 0.6853 Adjusted R Square 0.6015 Standard Error 120.7878 Observations 30 The coefficient of determination indicates what?
68.5% of the variance in stock price is explained by the independent variables
400
Starbucks is interested in decreasing customer wait times. They think that training employees according to a new set of procedures will decrease waiting times. To test the usefulness of the training, they pick two locations and have all employees at one location trained. Employees at the other location do not receive the training. They measure wait times for both locations one week after the training. Assuming the average wait time is significantly lower in the training location than the non-training location, how many conditions for causality are met in the above example? Which ones?
2 Timing (cause leads to effect) Significant statistical relationship (Reject the null)
400
What are the relative magnitudes of the mean, median, and mode for a unimodal distribution that is negatively skewed?
mean < median < mode
400
At a local gas station, attendants are supposed to check ID for anyone that looks younger than 40 years old when buying alcoholic products. Recently, an undercover agent observed the gas station for 8 hours and found that out of 200 customers that purchased alcoholic products 100 customers appeared to be younger than 40 years old. Ninety-five of those customers were asked for ID. Historically, these gas station attendants have checked 92% of customers looking younger than 40 years old. Has this gas station increased the checking of IDs for customers who appear younger than 40 years of age? What type of test? What are the hypotheses?
1 proportion z test Ho: p=.92 Ha: p>.92
400
The amount of Ozone in the atmosphere, although present in minute quantities, is critical to life because it absorbs harmful ultraviolet (UV) radiation coming from the sun. Ozone is known to be at its largest concentration in the lower stratosphere during January and February. Scientists, seeking to determine which month had the highest concentration, took Dobson spectrometer measurements from a random sample of base stations over a 15-year period for each of the two months. The monthly mean Ozone concentrations are shown in the table at right. What type of test? Hypotheses?
t-Test: Paired Two Sample for Means H 0 : Md(Jan-Feb) = 0, H 1 : Md(Jan-Feb) ≠ 0
400
You’ve decided that you want to be a business executive. You think you are very agreeable and are interested in determining wheather agreeableness affects the amount of money you are likely to make as an executive. To investigate this question, you collected data on executives’ pay (in dollars) and their level of agreeableness (1-7 point Likert scale). You did this for 100 executives. Below are the results of the simple regression you ran. What is the independent variable? Dependent Variable?
Agreeableness Executive Pay
500
Americans are known to be workaholics who often don’t use the vacation time that they are allowed. Some have wondered whether men or women have a greater tendency to be workaholics. A statistician designed a test to determine whether male or female employees used more of their vacation time. The study involved measuring the days of vacation used by one randomly selected male employee and one randomly selected female employee from each of the 30 departments of a Fortune 500 firm. Which of the statistical analyses would be the most appropriate for the statistician to use?
Matched pairs t-test
500
For which of the following research questions is one-way ANOVA the correct statistical technique to use to analyze the data? a. Are males and females equally likely to vote for the incumbent in the upcoming election? b. Do freshmen, sophomores, juniors and seniors at the university level spend the same amount of time on social media each week? c. Do Spring 2014 graduates have the same mean starting salaries as Fall 2013 graduates? d. Are a person’s height, average hours of sleep per week, and educational attainment correlated with income?
B
500
At a local gas station, attendants are supposed to check ID for anyone that looks younger than 40 years old when buying alcoholic products. Recently, an undercover agent observed the gas station for 8 hours and found that out of 200 customers that purchased alcoholic products 100 customers appeared to be younger than 40 years old. Ninety-five of those customers were asked for ID. Historically, these gas station attendants have checked 92% of customers looking younger than 40 years old. Has this gas station increased the checking of IDs for customers who appear younger than 40 years of age? What is the correct decision at alpha=.05?
Fail to reject the null hypothesis; conclude that the gas station has not increased the checking of IDs.
500
Banks in the United States are rated for safety and soundness using the CAMELS supervisory rating. The CAMELS supervisor rating ranges from 1-5, with a 1 assigned to the safest banks and a 5 given to banks deemed to be an imminent threat of failure. The FDIC assigns these ratings based on a ratio analysis of bank financial statements and on-site examinations, and uses these ratings to determine if it should intervene in a bank’s operations. If the appropriate null hypothesis is that a bank is safe and requires no intervention, which statement best describes a Type I error on the part of the FDIC?
Reject H 0 and intervene with the bank’s operations, when in reality the bank is safe and does not require intervention.
500
You’ve decided that you want to be a business executive. You think you are very agreeable and are interested in determining wheather agreeableness affects the amount of money you are likely to make as an executive. To investigate this question, you collected data on executives’ pay (in dollars) and their level of agreeableness (1-7 point Likert scale). You did this for 100 executives. A question on the test asks you "what would you predict happens to an executive’s pay for every 1 point increase in agreeableness?" Where on the output can you find this information?
The coefficient on "agreeableness" AKA the slope for agreeableness