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# The first two questions refer to the following information A

### Customer Question

The first two questions refer to the following information:

A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis.

If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is the appropriate pair of hypotheses in this case?
(a) Ho:μ1 -μ2=0
Ha:μ1 -μ20
Ha:μ1 -μ2=0

(c) Ho:μ1 =μ2
Ha:μ1 >μ2

(d) Ho:μ1 -μ2=0
Ha:μ1 -μ2>0

(e) Both (c) and (d) are correct.

The following is the (edited) output for the test:

Two-Sample T-Test and CI
sample N Mean StDev SE Mean
1(M) 112 7.38 6.95 0.66
2(F) 101 7.15 6.31 0.63

Difference=mu(1)-mu(2)
Estimate for difference: 0.230000
95% lower bound for difference: -1.271079
T-Test of difference: T-Value= 0.25 P-Value= 0.400 DF=210

From the output we learn that:
(a) the data provide sufficient evidence to reject H0 and to conclude that the mean depression score for male teens is larger than that of female teens.
(b) the data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score.
(c) the data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens.
(d) the data do not provide sufficient evidence to reject H0, so we accept it, and conclude that male and female teens do not differ in mean depression score.
Submitted: 5 years ago.
Category: Math Homework
Expert:  R.R. Jha replied 5 years ago.
Hi,

1) (e) Both (c) and (d) are correct.

2) (c) the data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens.

Regards