Question

Siegel (1990) found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who did not 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: 11,7,6,9,12,8,7

Dog Owner: 6,4,7,3,7

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

Note for problem above: Be sure and show a full diagram of the research design. Also show all steps and calculations you made for each test following the process outlined in the t-test formula sheet handout. What statistical decision do you make in each case? Finally report your results professionally in APA format (see last step of the formula sheet for this module).

Answer 1

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
      
Sample #1   ---->   1
mean of sample 1,    x̅1=   8.571
standard deviation of sample 1,   s1 =    2.225
size of sample 1,    n1=   7
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   5.400
standard deviation of sample 2,   s2 =    1.817
size of sample 2,    n2=   5
      
difference in sample means = x̅1 - x̅2 =    8.5714-5.4=   3.1714
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.0716
std error , SE =    Sp*√(1/n1+1/n2) =    1.2130
t-statistic = ((x̅1-x̅2)-µd)/SE =    (3.1714-0)/1.213=   2.6146
      
Level of Significance ,    α =    0.05
Degree of freedom, DF=   n1+n2-2 =    10
t-critical value , t* = ±   2.228   (excel formula =t.inv(α/2,df)
Decision:   | t-stat | > | critical value |, so, Reject Ho  
      
p-value =    0.0258   (excel function: =T.DIST.2T(t stat,df) )
Decision :   p-value <α , Reject null hypothesis  
Conclusion: There is enough evidence to conclude that there is a significant difference in the number of doctor visits between dog owners and control subjects   

This test is  found to be statistically significant, t(10) = 2.61, p < .05;