Question

Health self-evaluation as an indicator of general health was investigated in two groups of older adults. Older adults in one group were dog owners while in the second group older adults did not own dogs. Follow the 8-step hypothesis testing, using the information given below to determine if the two groups of older adults had different health self-evaluation scores. Use alpha level of .05. For all calculations, please keep two decimals.

Group	Sample Size (n)	Mean Health Evaluation Score	Std. Deviation
Dog Owners	18	62.5	6.5
Not a dog owner	17	58	5.7

Answer 1

Problem:
Hypothesis to determine if the two groups of older adults had different health self evaluation scores.

Null Hypothesis:
Ho:The mean difference of health self evaluation score for the 2 groups of older adults is same

Alternate Hypothesis:
H1:The mean difference of health self evaluation score for the 2 groups of older adults is not same.

We will test the hypothesis at 5% level of significance.

If |calculated test statistic|> t(/2,n1+n2-2) we reject the null hypothesis.

The following image will show the critical regionThe tabulated value of t using( n1+n2-2=18+17-2=33) 33 df and =0.05: 2.034515
The critical value is: 2.034515

The test statistics is given as:

Where Sp is the the pooled standard deviation which is given as:

x1=62.5
x2=58
Sp=6.13
t*=(62.5-58)/(6.13*(1/18+1/17)^0.5)

t*=2.17 : The value of test statistic.

Since |calculated t|(2.17)> tabulated t(2.034515) we reject Ho at 5% level of significance.

Conclusion:  Hence we conclude that the mean difference of health self evaluation score for the 2 groups of older adults is not same.