Psychology 122: Statistics for the Behavioral Sciences - Suggested Problems
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Key Terms:
solutions
  1. A psychologist is wondering undergraduates' attitudes towards marriage are related to the nature of their parents' relationship. Determine the independent and dependent variables in this study. Provide an operational definition for each variable and identify whether it would be a categorical or continuous variable. Is your research design experimental, or observational?
   
MCTs and Variability:
solutions
  1. A study examines the relationship bretween level of arousal and problem sovling. three samples are used, consisting of subjects with low, moderate, or high levels of arousal. The researcher measures the number of problems successfully completed during a problem solving task. The data appear in the table below. Calculate the mean, median, mode, and standard deviation for each sample.
    Low Arousal
    Moderate Arousal
    High Arousal
    2
    20
    9
    6
    17
    8
    5
    14
    8
    7
    16
    6
    5
    18
    7
    5
    19
    10
    4
    14
    6
    4
    16
    8
    7
    18
    7
    6
    18
    8
  2. What do the values that you calculated in question #1 tell you about the shapes of the distributions for the three arousal levels?
   

 Z-scores:
solutions

  1. Find the following:
  1. P(z >1.57)
  2. P(z < -1.57)
  3. P(-.24 < z < 1.98)
  4. P(.24 < z < 1.98)
  1. Let's pretend that the average college student procrastinates 12 times a day. Let's further pretend that the distribution procrastination incidents for college students is distributed normally with a standard deviation of 2.5 incidents. Finally, let's pretend that you procrastinated 8 times yesterday, not including frequent snack breaks which are necessary to maintain optimum health. What is your percentile rank? Interpret this value.
   

 Confidence Intervals:
solutions

1. Researchers have developed a filament that should add to the life expectancy of light bulbs. The standard 60-Watt bulb burns for an average of mu = 750 hours with sigma = 20. A sample of 100 bulbs is prepared using the new filament. The average life for this sample is 820 hours.
  1. Make an interval estimate so that you are 80% confident that the true mean is in your interval.
  2. Make an interval estimate so that you are 99% confident that the true mean is in your interval.
2. A survey of students produced the following data regarding their age when they first consumed an alcoholic drink: 11, 13, 14, 12 and 10.
  1. Find the 95% CI for the population mean.
  2. Compre the 99% CI for the populariong mean.
  3. Compare the results in parts a and b. What general statement an be made about the level of confidence and the interval width.
   

  One-Sample Hypothesis Tests:
solutions

  1. The athletic department wants to see how student athletes at AC compare with the general student body. Let's assume that the average SAT score for incoming AC students is 1250. The athletic department conducts a survey of 61 randomly selected student athletes and finds that the average SAT score of the sample is 1284 with a standard deviation of 90 points. Do these data provide enough evidence to conclude that student athletes differed from the general student body in their performance on the SAT (set alpha = .01)?
  2. After seeing how successful it was in the Olympics, I decide to start taking Nandrolone - some kind of steroid - in an effort to improve my professoring. I am a little nervous because I have heard that steroids are bad for you, so I want to be sure that the drugs actually work. I know that, on average, I publish approximately 1 journal article per year. Let's say that over the next five years (n = 5), I publish an average of 1.34 papers per year while taking Nandrolone; s = .50. Do these data suggest that I should continue taking the Nandrolone? In other words, did the steroid improve my publication rate? Perform a two-tailed test with alpha = .05.
  3. I had a dream last night about my father. It's peculiar. I'm 20 years older now than he ever was, so in a sense, he was the younger man. That got me to thinking about dreams, and whether I remembered more or fewer dreams than average. I kept a dream journal; every morning for a week, I recorded the number of dreams I remembered from the previous night's sleep. The data are as follows, 5, 3, 6, 4, 0, 6,4. Do these data suggest that I remember more or fewer dreams than average if, according to Susan Boyle's book "I Dreamed a Dream of Days Gone By", the average person remembers 2.6 dreams per night?

 

 

   

 Two-Sample Independent Hypothesis Tests:
solutions

  1. Hewlett Packard and Epson each claim to have the fastest printers on the market. An independent laboratory decides to test which company makes the faster printer. They print 100 5-page documents on each printer, and measure the amount of time required to complete each job. The mean print time for the HP machine is 150 s with a standard deviation of 50 s; the mean print time for the Epson machine is 165 s with a standard deviation of 75 s. Conduct a two-sample hypothesis test to determine which printer is faster. Set alpha = .05.
  1. Would you change your decision regarding the null if alpha = .10?
  1. Find the 95% CI for the true difference in speed between the two printers. Does the interval make sense in light of your decision regarding the null in question 1?
   

 Paired Hypothesis Tests:
solutions

  1. An advertising company is interested in determining whether their new jingle will make people feel happy. They amass a group of 120 consumers and ask each one to rate their mood on a scale from 1 (woefully depressed) to 100 (gleefully elated). The average score before hearing the jingle was 66.2, and the average score after viewing the commercial was 69.4; the standard deviation of the difference score was 12.2. Do these data provide convincing evidence that the jingle influenced the consumers' moods? Set alpha = .01.
  2. What is the 99% CI for the average difference in voter intentions before and after viewing the commercial?
   

  One-Way ANOVA:
solutions

  1. Jet lag can be quite inconvenient, especially for international business travelers. There has been some debate about whether jet lag effects differ depending on whether on is traveling East or West. The data below represent people's judgements of the severity of their jet lab symptoms after recent trips either East, West, or within the same time zone.

    2.  
    East
    West
    Same
     
    2
    6
    1
     
    1
    4
    0
     
    3
    6
    1
     
    3
    8
    1
     
    2
    5
    0
     
    4
    7
    0
           
     
    Use the data in the table above to determine whether there is enough evidence to conclude that jet lab effects are more severe traveling in one direction than another. Set alpha = .05. Fcrit = 3.68.
  2. Calculate Tukey's HSD and determine which flight conditions differ from one another; qcrit = 3.67.
   

  Repeated Measures ANOVA:
solutions

  1. How do repeated measures experiments differ from between measures experiments?
  2. How does the analysis of a RM-ANOVA differ from the analysis of a BS-ANOVA?
   

  Two-Way ANOVA:
solutions

Omnibus Test
Source df SS MS F p-value
Model 8 .0372
Error 99 5.00
Total 639
Individual Effects
Source df SS MS F p-value
A 2 28.0 .0496
B 2 16.0 .3428
AxB 100.0 .0215
  1. Base your answers to the following questions on the ANOVA tables above.
    1. Fill in the blanks in the above ANOVA tables.
    2. How many levels for Factor A?
    3. How many levels for Factor B?
    4. How many total units in the experiment?
    5. How many units per treatment?
    6. Which factors are significant?
  2. Time of day is believed to influence cognitive performance, but for many years, most memory experiments were conducted in the later afternoon when college students were most alert. This might have led researchers to overestimate how much memory declines as we age because older adults tend to be less alert in the late afternoon than in the morning. An experiment was conducted in which older and younger adults took a memory test either in the early morning or the later afternoon. Conduct a complete 2-Way ANOVA using the data below to determine if time of day influenced cognitive performance differently in younger and older adults. Higher scores indicate better performance. Fcrit for the omnibus test is 3.10; Fcrit for the main and interaction effects is 4.35.
Older Adults
Younger Adults
AM Test
PM Test
AM Test
PM Test
2
2
5
10
4
1
5
9
3
1
1
9
4
3
3
6
4
2
7
10
7
3
3
10
.
   

Simple Regression:
solutions

  1. One argument for eating veggies is that they are not calorically dense. In other words, you have to eat like 1,000 carrots to equal the number of calories in one sweet, delicious, Oreo cookie.
    2. Sum (x)
    Veg. Cons    		 Sum (y)
    Weight    		 Sum(x2) Sum (y2) Sum (x*y)
    109.5 11,087 246.25 1,666,795 15,013
    1. Caculate the regression equation that describes the relationship between vegetable consumption and weight for the data depicted above (n = 77).
    2. How many pounds would one expect to lose if one ate one additional serving of vegetables per day?
    3. Based on our model, what is the expected weight of a person who eats 3 servings of vegetables per day?
    4. Calculate the correlation coefficient and the coefficient of determination. What do these value suggest about the predictive ability of vegetable consumption?
  1. Use SPSS to examine how well weekday bedtime predicts weekend bedtime.
    1. What is the regression equation that describes the relationship.
    2. How many additional hours later would you expect one to go to bed on the weekend if they went to sleep one hours later during the week?
    3. Based on our model, what is the expected weekend bedtime of someone who went to sleep at midnight during the week?
    4. Is weekday bedtime a significant predictor of weekend bedtime?
    5. Calculate the correlation coefficient and the coefficient of determination. What do these value suggest about the relationship of the two variables?
   

  Correlation:
solutions

  1. In the latest labor negotiations, Biff told his workers at the widget factory to work faster without making mistakes. When one of the labor unions lawyers argued this was impossible, Biff asked her to prove it. The lawyer submitted the data below as proof. Use these data to find the correlation coeffecient that relates average widget making speed (RT) with the number of errors made.
    2.  x (rt) y (errors) x2 y2 s*y
    184 10
    213 6
    234 2
    197 7
    189 13
    221 10
    237 4
    192 9
    Sum (x) = 1667 Sum (y) = 61
  2. Use SPSS to determine whether the correlation coefficient is significantly different from zero. [Hint: you can check your calculations for part 1) by determining whether SPSS returns the same value for r]
   

  Multiple Regression:
solutions

  1. SMS, everyone's favorite stats honor fraternity, is tired of spending so much time evaluating pledges during rush. So, they decide to construct a multiple regression equation that will allow them to predict the potential of pledges based on a small number of predictor variables including:
    GPA, GPA in math courses, # of pocket protectors, # of Star Trek conventions attended in past year, # of t-shirts with clever mathematical puns, and # of friends outside of SMS. The regression equation was derived by rating ALL current members "success" on a 100 point scale, and collecting data about the 6 predictor variables. Use the resulting SPSS output below to answer the following questions. Assume that a = .05.
    2. Source
    df
    Sums of Squares
    Mean Square
    F
    p-value
    Model
    6
    180.00
    60.00
    6.00
    .0125
    Error
    36
    180.00
    5.00
    		 
    Total
    42
    360.00
    		      

    Variable
    df
    Parameter Estimate
    Standard Error
    Observed t
    p-value
    Intercept
    1
    22.00
    2.35
    9.36
    .0001
    GPA
    1
    -.016
    0.57
    -0.28
    .3216
    GPA-Math
    1
    2.17
    0.37
    5.86
    .0027
    Protectors
    1
    4.81
    3.14
    1.53
    .1349
    StarTrek
    1
    6.03
    1.38
    2.30
    .0375
    T-shirts
    1
    0.88
    0.42
    2.10
    .0462
    Friends
    1
    -3.25
    0.49
    -6.63
    .0001

    1. Will the overall model help the Rush Chairperson pick appropriate pledges? Explain.
    2. What is R-squared?
    3. What is the regression equation suggested by this output?
    4. The Rush Committee decides that it will only initiate pledges with predicted score of 50. Your younger brother has an overall GPA of 3.20, his Math GPA = 3.80, he has 2 pocket protectors, has attended 2 Star Trek conventions, owns 12 t-shirts with math puns, and has 2 friends. Will he be offered a coveted spot in the fraternity?
   

  Chi-Squared:
solutions