Fill out one student questionnaire and adminster the questionnaire to three friends.
Enter the data from the questionnaires. Click here for further instructions.
Homework #1
I recently read a study designed to determine if exercise reduced depression in college students. A group of students was selected randomly from the campus directory. They rated their mood on a 10-point scale and indicated how many hours a week they went to the gym. The researchers found that, in general, people who spent more time in the gym reported being in better moods than people who spent less time in the gym. For the described study, please identify the independent and dependent variables along with the operational definition for each. Was the study observational, or experimental? Can the researchers draw a cause-and-effect relationship between the variables of interest? If not, propose an alternative explanation for the reported results.
Make a bar graph (frequency table) for the favorite Cable Channel data (click here for an SPSS: graphing tutorial).
The numbers that follow represent the total number of hours of sleep that I have received each night for the past week: 6, 7, 7, 6, 7, 4.5, 8. Find, the mean, median, mode, variance and standard deviation for these data. Show your work.
Make a histogram either by hand or with SPSS/Excel (click here for an SPSS: graphing tutorial) of the weekend and weekday bedtime data. Use SPSS to find the mean, median, mode, variance and standard deviation for the weekend and weekday bedtime data (SPSS: descriptive statistics). Do these data suggest that bedtime is symmetrical, positively-skewed, or negatively-skewed? Why?
Homework #2
My friends back in college were named John, Paul, George, Ringo, Belinda, Jane, Gina, Kathy, and Charlotte.
Are A and B independent? Justify your answer and explain.
The Amherst Police Dept. has developed a new test to determine whether a driver is legally drunk. The probability of obtaining a positive test given that a driver is drunk is .90; the probability of obtaining a positive test given that the driver is sober is .05. Use Bayes' Theorem to determine the probability that a person is drunk given that the test registers positive. Assume that 20% of drivers who are pulled over are in fact drunk.
Construct a probability distribution table for the siblings data (SPSS can do this for you if you follow the first six steps of the SPSS graphing tutorial, substituting 'siblings' for the bedtimes, etc.). Use the probability distribution table to calculate the expected value and standard deviation for the distribution.
You choose three marbles from a bag containing 10 marbles: 6 red and 4 blue. What is the probability that exactly 2 are blue? Assume that the selection is done with replacement.
Imagine that the 'game' you played in #4 was changed such that the selection was done without replacement. What is the probability that only one of the three marbles selected was blue?
Use z-scores to determine the probability that an Amherst student is at least 5'3". Hint: Use SPSS to find the mean and SD of the distribution (SPSS: descriptive statistics); then calculate a z-score and consult the z-score table.
Use z-scores to determine the proportion of Amherst students that are between 5'4" and 6'0" (i.e., at least 5.4", but not taller than 6'0"). Use the same procedure as in #6.
Bonus: As I'm sure most of you know, John, Paul, George, and Ringo are the Beatles. Who are Belinda, Jane, Gina, Kathy, and Charlotte?
Homework #3
Find the 95% CI for the number of hours of classes skipped per semester by the average Amherst Student. Use SPSS to find the mean and standard deviation (SPSS: descriptive statistics), but calculate the CI by hand. Check your CI using SPSS and attach the SPSS ouput (SPSS: CIs).
Use the data from question #3 in homework assignment #1 to determine the 90% and 95% CI for the average number of hours of sleep per night that I obtained.
How many Amherst students would we need to interview in order to estimate the quantity in #1 within +/- 1 hour?
Fill in the blanks: According to the central limit theorem, the ___________ distrubtion of a population will be approximately _________ if n is sufficiently large (n > ______). Also, the population parameter should be equal to the mean of the ___________ and the ____________ will be equal to s / sqrt (n).
Provide two reasons why large samples of data are generally preferred over small samples of data.
Homework #4
You get a job as a traveling salesperson for Callahan Brake pads. You try to sell your first client on the idea that Callahan Brake pads are superior in quality. The client is concerned about price. So, you conduct a study to convince him that Callahan brake pads do not cost any more or less than the average brake pad. Callahan Brakes pads cost $15 per pair. The average cost of your 5 leading competitors $13.62 with s = 1.09. Conduct a one-sample hypothesis test (alpha = .05) to determine if the cost of Callahan Brake pads are in fact different from average.
Use SPSS to determine if Amherst students are eating enough fruit. Assume that the USRDA is 3 pieces of fruit. Set alpha = .01 (SPSS: 1-sample T Test).
You and Biff are playing a heated game of Jacks, when the conversation invariably turns to who is the superior player. You both know enough statistics to know that one game won't settle the matter completely. So, you each play six games, you pick up 5, 4, 8, 4, 5, and 6 jacks. Biff picks up 4, 4, 5, 3, 4, and 5 jacks. Conduct a two-sample t-test (alpha = .05) to determine who is the better jackster. Do the calculations by hand, but you may check your work with SPSS (SPSS: Independent T Test).
Use SPSS to perform a two-sample t-test to determine if Amherst students consume different amounts of fruits and vegetables (hint: is this a paired test or an independent test?). Set alpha = .01.
Use SPSS to determine whether females and males consume the same amount of vegetables? Set alpha to be an appropriate level (SPSS: Independent T Test).
Homework #5
Use SPSS to perform a one-way ANOVA to determine whether the form of the question (average pounds of paper discarded) influenced people's estimates of how many pounds of paper they discarded. Be sure to report the results of your test in the proscribed manner and to conduct post-hoc comparisons if warranted. Set alpha = .05.
Use SPSS to perform a Repeated Measures ANOVA to answer question #4 from HW #4. Remember, you can do ANOVA with only two groups, but you can't do a t-test with more than 2 groups). How does your answer to this question compare with your answer from Homework #4? Does your decision regarding the null change? What is relationship between the observed values of the two test statistics?
Bristol-Meyers Squib, the company that makes Pepto-Bismol, wants to capitalize on the Thanksgiving Holiday. Last year, they ran a study to determine whether eating the big Thanksgiving meal at different times of day would influence the experience of indigestion. The data, which represent discomfort ratings at 11:00 pm are presented in the table below. Higher ratings indicate more discomfort. Conduct a one-way ANOVA to determine if meal time influences indigestion. Be sure to report the results of your F-test in the proscribed manner and to conduct post-hoc tests if warranted. Based on the results of your test, would it be valuable for BMS to try to influence the American people? If so, how? Fcrit = 4.26; q = 3.95.
2:00
4:00
6:00
x
x^{2}
x
x^{2}
x
x^{2}
7
4
10
8
5
8
7
3
9
9
5
6
Homework #6
Use SPSS to perform a Two-Way ANOVA looking at the effects of gender (Male vs. Female) and school year on the number of trips students make into town. To make life simpler, use the new variable 'Upper' for class year (it divided everyone into two groups (Young - Frosh and Sophs; Old = Juniors and Seniors).
A small study was conducted to examine whether the number of children that someone planned to have was related to either their gender (Male vs. Female), or the size of the family in which they grew up (Small vs. Large). The data are presented in the table below. Conduct a Two-Way ANOVA by hand to determine if there is a significant relationship between the variables in question (set alpha = .05). For the omnibus test, F_{crit} = 3.24; for the main effects and interaction effect test, F_{crit} = 4.49.
Small
Large
Male
3, 2, 3, 4, 3
5, 4, 5, 2, 4
Female
4, 3, 4, 1, 3
1, 2, 1, 0, 1
Small
Large
Male
x
x^{2}
x
x^{2}
3
5
2
4
3
5
4
2
3
4
Small
Large
Female
x
x^{2}
x
x^{2}
4
1
3
2
4
1
1
0
3
1
Homework #7
You and Biff were sitting around one weekend evening, sipping on some age-appropriate refreshments; let's refer to these age-appropriate refreshments as 'beer'. You noticed that as you drank more and more refreshments, your need to visit the bathroom (BR) increased. What are you going to do? You decide to collect some data. The table below presents information on a randomly selected sample of students for whom two pieces of data were collected: the number of refreshing beverages consumed in an evening, and the number of trips to the BR. Use these data to perform the following calculations:
What is the linear regression relating beer consumption and trips to the BR?
How many trips to the BR would you predict someone would make if they consumed 5 beers? Could you make a prediction for someone who tossed down a 12-pack?
Perform a test to determine whether the number of beers consumed a significant predictor of trips to the BR.
What is the correlation coefficient?
How much of the variance in trips to the BR can be explained by beer consumption?
Beers
Visits to the BR
3
0
4
2
5
5
4
6
7
8
4
2
6
4
5
3
7
5
5
5
2. Use SPSS to conduct a simple regression analysis to demonstrate that your calculations for question 1a, c, d, and e, are correct. Simply highlight the relevant locations on the SPSS output and label them with the appropriate letter (a, c, d, and e). To do this, you will need to create your own SPSS data set.
3. Use SPSS to perform a multiple regression analysis to determine which of the following factors predict # of visits home per semester: distance from parents home to Amherst, high school friends in contact, # of brothers, # of sisters, # of cars on campus. What factors would you include in the the best-fit model? What is R-squared for the best fit model? Does the best-fit model allow one to predict # of visits home better than chance?