SOLUTION: A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages µ = 40 on a standardized depressio

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Question 364879: A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages µ = 40 on a standardized depression test.
The psychologist obtains a sample of n = 9 individuals who are all older than the age of 70. the 37,50,43, 41,39,45,49,44,48. on the basis of this sample
, can the psychologist conclude that depression for elderly people is significantly different from depression in the general population? Use a two-tailed test at the .05 level of significance.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: mu=40 (no diff from general population)
Ha:mu%3C%3E40 (diff from general population)
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alpha=0.05
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sample info n=9, xbar=44, s=4.5
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statistic t=%28xbar-mu%29%2F%28s%2Fsqrt%28n%29%29=%2844-40%29%2F%284.5%2Fsqrt%289%29%29=-2.67
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critical value: t%5Bc%5D=t%5B.05%2C8%5D=-+2.31
pvalue=0.028
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Since statistic =-2.67 exceeds the critical value or since pvalue%3Calpha
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Conclusion: Reject Ho and report that depression for elderly people is significantly different from depression in the general population