A Canadian study measuring depression level in teens (as reported in the Journal

Question

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. The following is the (edited) output for the test: From the output we learn that: Selected Answer: 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. Answers: 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.

Explanation / Answer

here null hypothesis H0:male and female teens do not differ in mean depression score. and

alternate hypothesis Ha:  mean depression score for male teens is higher than for female teens ( one tailed)

here sample size is large ( more than 30) , so we can us z-test of difference of sample means and

statistic z = (x1- x2-)/sqrt(12/n1+22/n2)

if calculated z will be more than one tailed critical z(0.05)=1.6449, then we fail to accept H0 and conclude that

mean depression score for male teens is higher than for female teens at 5% level of significance and right choice will be 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.

other wise right choice will be

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.

(if find any difficulty please respond back)

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