Question

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.
[ _________, __________ ]

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