SOLUTION: A study examines self-esteem and depression in children. A sample of 25 children with low self-esteem is given a standardized test for depression. The average score for the group i

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Question 1183497: A study examines self-esteem and depression in children. A sample of 25 children with low self-esteem is given a standardized test for depression. The average score for the group is M = 93.3. For the general population, scores on the depression test form a normal distribution with a mean of µ = 90 and a standard deviation of σ =15. Do children with low self-esteem show significantly more depression?
Found 2 solutions by Boreal, robertb:
Answer by Boreal(15235) About Me  (Show Source):
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Assuming random sample
Ho: mu is 90
Ha: mu is not = 90 (two way test)
alpha can be 0.05 p{reject Ho|Ho true}
test is a z
critical value reject Ho if |z| > 1.96
calculation, z=(x bar-mean)/sigma/sqrt(n)
z=3.3*sqrt(25)/15
=16.5/15
=1.1
fail to reject Ho at the 5% level; insufficient evidence to reject null hypothesis that mean is truly90

Answer by robertb(5830) About Me  (Show Source):
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H%5B0%5D%3A+mu+=+90
H%5Ba%5D%3A+mu+%3E+90
The alternative hypothesis was mu+%3E+90 since the test specifically asked if low self-esteem shows significantly more depression.
(The assumption being, the higher the score indicates greater level of depression.)
Since significance level is unspecified we use alpha+=+0.05.

==> p-value = 0.136, from https://stattrek.com/online-calculator/normal.aspx.
Since+p-value+=+0.136+%3E+0.05+=+alpha, do not reject H%5B0%5D,
and conclude that children with low self-esteem doesn't necessarily have greater depression.