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Statistics Exercise II: Statistical inference, 1- and 2-sample t-tests

These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

#1.  Define "power" in relation to hypothesis testing.

#2.  Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?

#3.  In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test.

1. A study testing whether night-shift workers sleep the recommended 8 hours per day
2. A study measuring differences in attitudes about morality among Democrats and Republicans
3. An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule

Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions.  Round your answers to the nearest dollar, percentage point, or whole number.  
 
#4.  Test the age of the participants (AGE1) against the null hypothesis H0 = 34.  Use a one-sample t-test.  How would you report the results?
 
a.         t = -1.862, df = 399, p > .05 
b.         t = -1.862, df = 399, p < .05 
c.         t = 1.645, df = 399, p > .05 
d.         t = 1.645, df = 399, p <  .05 

#5.  What is the mean and standard deviation for the Lifestyle score (L)?
 
a.  31.22, 7.99 
b.  36.19, 8.54 
c.  30.03, 7.28 
d.  55, 13

#6.  The first case shown in the data file is a firefighter with a financial Risk-Taking score (R) of 38.  What is his Risk-Taking z-score (hint: you will need to find the Risk-Taking mean and standard deviation)?
 
a.  0.179 
b.  -0.223 
c.  1.342 
d.  -1.223
 
#7.  Perform independent sample t-tests on the Lifestyle, Dependency, and Risk-Taking scores (L, D, and R) comparing men and women (GENDER1).  Use p < .05 as your alpha level and apply a two-tailed test.  On each of the three scales, do men or women have a significantly higher score?
 
a. Lifestyle: Men, Dependency: Women, Risk-Taking: Men.
b. Lifestyle: Not significantly different, Dependency: Women, Risk-Taking: Men 
c. Lifestyle: Women, Dependency: Women, Risk-Taking: Men 
d. Lifestyle: Men, Dependency: Men, Risk-Taking: Not significantly different
 
#8. The median US salary is $50,700, according to US Census data. Using a one-sample t-test, test to see if participant income (INC1) is different from the national average. Use a two-tailed test and an alpha level of 5%.

1. Participant income is significantly greater than the national average
2. Participant income is significantly less than the national average
3. Participant income is not significantly different from the national average

Participant income cannot be compared to the national average