Statistics

I need help with my week 5 assignment for statistics

Post Merge: 10 years ago

1.   Warm up those calculators!   Using the following information, calculate the t-test statistic by hand.

a.    1 = 62    2 = 60   n1 = 10      n2 = 10      s12 = 6      s22 = 10

t= x1-x2/ the square root of (s1^2/n1+ s2^2/n2)
62-60/the square root of 6/10+ 10/10
2/the square root of .6+ 1
2/the square root of 1.6
square root of 1.6=1.26
2/1.26= 1.58
t=1.58

b.    1 = 158    2 = 157.4   n1 = 22      n2 = 26      s12 = 4.23   s22 = 6.73


c.    1 = 200    2 = 198   n1 = 17      n2 = 17      s12 = 6      s22 = 5.5


2.   Using the results you got from question 1 above, and a level of significance at .05, what are the two-tailed critical values associated with each? Would the null hypothesis be rejected?




3.   Here’s a good one to think about. A public health researcher tested the hypothesis that providing new car buyers with child safety seats will also act as an incentive for parents to take other measures to protect their children (such as driving more safely, child-proofing the home, etc.). Dr. Joy counted all the occurrences of safe behaviors in the cars and homes of the parents who accepted the seats versus those who did not. The findings? A significant difference at the .013 level. Another researcher did exactly the same study, and for our purposes, let’s assume that everything was the same – same type of sample, same outcome measures, same car seats, and so on. Dr. Keel’s results were marginally significant (review chapter 9) at the .051 level. Whose results do you trust more and why?







4.   The results of the following three experiments where the means of the two groups being compared are exactly the same but the standard deviation is quite different from experiment to experiment. Compute the effect size using the formula on page 198 and then discuss why this size changes as a function of the change in variability.

 
Experiment 1   Group 1 Mean   78.6   Effect size =      
   Group 2 Mean    73.4         
   Standard Deviation   2         
Experiment 2   Group 1 Mean   78.6   Effect size =      
   Group 2 Mean   73.4         
   Standard Deviation   4         
Experiment 3   Group 1 Mean   78.6   Effect size =      
   Group 2 Mean   73.4         
   Standard Deviation   8      






5.   In the following examples, indicate whether you would perform a t test of independent means or dependent means.

Two groups were exposed to different levels of treatment for ankle sprains. Which treatment was most effective?



A researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas others received the standard amount.



A group of adolescent boys was offered interpersonal skills counseling and then tested in September and May to see if there was any impact on family harmony.



One group of adult men was given instructions in reducing their high blood pressure whereas another was not given any instructions.


One group of men was provided access to an exercise program and tested two times over a 6-month period for heart health.




6.   In a study comparing individual performance with group performance, Laughlin, Zander, Knievel, and Tan found that groups consistently outperformed the best of the individuals. The task was a letters-to-numbers problem in which an arithmetic problem was presented substituting a letter in place of each digit. Participants had to determine which letters correspond to each number. Three-person groups competed with individuals and scores were compared for the groups and the best of individuals. The dependent variable was the number of trials needed to solve each problem. The following data are similar to those obtained in the study.
            
 
Groups   Individuals      
n=15   n=15      
M=3.8   M=4.7      
SS=15.4   SS=18.2   
 
Based on these results, is there a significant difference between the performance for individuals versus the performance for groups? Use a two-tailed test with α=.05.













5.    Siegel found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who didn’t own pets. Similarly, consider the following hypothetical data. A sample of elderly dog owners is compared to a similar group (in terms of age and health) who do not own dogs. The researcher records the number of visits to the doctor during the past year for each person. The data are as follows:
 
Control Group   Dog Owners      
12   8      
10   5      
6   9      
9   4      
15   6      
12         
14      

Is there a significant difference in the number of doctor visits between god owners and control subjects? Use a two-tailed test with α=.05.