Homework SourseA study comparing attitudes toward death was conducted in wh
A study comparing attitudes toward death was conducted in which organ donors were compared with non-donors. A scale measuring death anxiety was administered with higher scores indicating more anxiety. Participants for each group were randomly selected. Non-donors (n=69) had a mean anxiety of 7.62 with a standard deviation of 3.45. Donors (n=25) had a mean of 5.36 with a standard deviation of 2.91. Do donors and non-donors anxiety levels differ? (8 pts)
What are the null and the alternative hypotheses?
Are the assumptions necessary for inference met?
Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared your t-statistic to.
State your conclusion.
Solution
Let
group 1 = non donors
group 2 = donors
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
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Yes, the conditions for inference are met.
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At level of significance = 0.05
As we can see, this is a two tailed test.
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Calculating the means of each group,
X1 = 7.62
X2 = 5.36
Calculating the standard deviations of each group,
s1 = 3.45
s2 = 2.91
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 69
n2 = sample size of group 2 = 25
Thus, df = n1 + n2 - 2 = 92
Also, sD = 0.714999301
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 3.160842252
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = +/- 1.986086317
As out t is not between the critical values, WE REJECT THE NULL HYPOTHESIS.
Thus, there is significance evidence that the donors and non-donors anxiety levels differ. [CONCLUSION]
