A researcher uses a matched-subjects design to investigate whether single people

Question

A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. Am inventory questionnaire is administered to a group o 20- to 29-year-old non-pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non-pet owners lor income, number ot close friendships, and general health. The data are as follows. Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with alpha =.05 for two tails. Construct the 95% confidence interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non-pet owners. (You should find that a mean difference of mu_D = 0 is an acceptable value, which is consistent with the conclusion from the hypothesis test.) There is some evidence suggesting that you are likely

Explanation / Answer

a)

Let ud = u(pet) - u(nonpet).              

Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/   0  

At level of significance =    0.05          

As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    1.954016842          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.797724035          
              
Calculating the mean of the differences (third column):              
              
XD =    2          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.507132682          
              
As df = n - 1 =    5          
              
Then the critical value of t is              
              
tcrit =    +/-   2.570581836      
              
Thus, as t < 2.5706, we   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Hence, there is no significant difference at 0.05 level between that mood scores for non-pet and pet owners. [CONCLUSION]

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b)

For the   0.95   confidence level,      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    2.570581836          
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    -0.050614915          
upper bound = [X1 - X2] + t(alpha/2) * sD =    4.050614915          
              
Thus, the confidence interval is              
              
(   -0.050614915   ,   4.050614915   ) [ANSWER]

As 0 is included in this interval, then there really is indeed no significant difference.
              
              
              

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