Question
A public health official hypothesizes that depression levels in the nation have been decreasing over the...
A public health official hypothesizes that depression levels in
the nation have been decreasing over the years. In the late 1990s,
the average score on the Birk Depression Inventory (BDI) in the
nation was 17 with a standard deviation of 6.3. A current sample of
17 produces a mean BDI score of 14.4. What can be concluded with α
= 0.10?
a) What is the appropriate test statistic?
na z-test one-sample t-test independent-samples t-test
related-samples t-test
b)
Population:
current sample the BDI score the nation the years depression
levels
Sample:
current sample the BDI score the nation the years depression
levels
c) Obtain/compute the appropriate values to make a
decision about H0.
(Hint: Make sure to write down the null and alternative hypotheses
to help solve the problem.)
critical value _________= ; test statistic =
_________
Decision: ---Select--- Reject H0 Fail to reject H0
d) If appropriate, compute the CI. If not
appropriate, input "na" for both spaces below.
[ _________, __________ ]
Homework Answers
Answer #1
(a) z-test (as populations sd is given)
(b) Population: the nation
Sample : current sample
(c) Ho: 
= 17
ha:
< 17
Test statistics
z = -1.7016
Critical Value of Z (LeftTailed): - 1.28
As the z stat (-1.7016) falls in the rejection area, we reject the Null hypothesis.
Hence we have sufficient evidence to believe that the mean BDI score is less than 17.
(d) CI = mean +/- E
Z Value for 90% CI = 1.645
CI = 14.4 +/- 2.514
CI = 11.886 , 16.914
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