Psychological Statistics

Psychology 400-102

Spring 2007 – Homework #7

Dr. Hitlan

Name________________________________

­­­­

1.  The null hypothesis in the one sample case is a statement of (1-point)

            a.  agreement with the research hypothesis

            b.  rejection

            c.  acceptance

            d.  no difference

2. In what circumstances is the t statistic used instead of a z-score for a hypothesis test? (1-point)

            a.  The t statistic is used when the sample size is n = 30 or larger.      

            b.  The t statistic is used when the population mean is unknown.       

            c.  The t statistic is used when the population variance (or standard deviation) is unknown.  

            d.  The t statistic is used if you are not sure that the population distribution is normal.

3.  On average, what value is expected for the t statistic when the null hypothesis is true? (1-point)

            a.  0    

            b.  1    

            c.  1.96           

            d.  t > 1.96

4.  Do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? The appropriate test of hypothesis would be (1-point)

            a. a one-tailed test

            b. a two-tailed test

            c. cross-sectional

            d. participant observation

5.  With α = .05 and df = 8, the critical value for a one-tailed t test is t = 1.860. Assuming all other factors are held constant, if the df value were increased to df = 20, the critical value of t would __________. (1-point)

            a.  increase      

            b.  decrease     

            c.  stay the same         

            d.  not enough information to answer

6. A sample of n = 25 scores produces a t statistic of t = –2.06. If the researcher is using a two-tailed test with α = .05, the correct statistical decision is __________. (1-point)

            a.  The researcher can reject the null hypothesis with α = .05 but not with α = .01.                

            b.  The researcher can reject the null hypothesis with either α = .05 or α = .01.          

            c.  The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.          

            d.  It is impossible to make a decision about H₀ without more information.

7. A sample is selected from a population with μ = 60 and a treatment is administered to the sample. After treatment, the sample mean is M = 66 with a sample variance of s² = 100. Based on this information, the size of the treatment effect, as measured by Cohen's d, is __________. (1-point)

            a.  d = 0.06     

            b.  d = 0.60     

            c.  d = 0.66     

            d.  Cohen's d cannot be computed without knowing the sample size.

8.  How does the shape of a t distribution compare with the normal distribution? How does the shape of a t distribution depend on sample size (n)? (3-points)

9.  A nutrition store in the mall is selling “Memory Booster” which is a concoction of herbs and minerals that is intended to improve memory performance. To test the effectiveness of the herbal mix, a researcher obtains a sample of n = 16 people and has each person take the suggested dosage each day for 4 weeks. At the end of the four-week period, each individual takes a standardized memory test. The scores from the sample are provided below.

In the general population, the standardized test is known to be normally distributed and have a mean of μ = 20. Do the sample data provide evidence that the Memory Booster improves memory performance? Test with α = .05.

(Show All Work)

20, 28, 30, 18, 30, 28, 26, 31, 23, 34, 20, 24, 22, 21, 26, 27

a. What is the null hypothesis (in words)? (1-point)                                                                                                                                                                                                                                                                                           

b. What is the research hypothesis (in words)? (1-point)                                                                                                                                                                                                                                                                                                

c. What is the t-critical value for rejecting the null? (1-point)                                                                                          

d. What is the t-obtained value (test statistic)? (4-points)                                                                                                        

e. Do you reject or fail to reject the null hypothesis? (1-point)                                                                                               

f. What type of error might you be making? (1-point)                                                                                                      

g. Based on your findings, what would you conclude (be specific and relate back to question)? (2-points)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

h. What is the size of the effect (Cohen’s d)? (2-points)                                                                                                        

i. Does the effect size index computed above represent a small, medium, or large effect? (1-point)