The following is the (edited) output for the test: A Two-sample T-Test and CI for the data. Sample 1(M) has N=112, Mean=7.38, StDev=6.95, SE Mean=0.66. Sample 2 (F) has N=101, Mean=7.15, StDev=6.31, SE Mean = 0.63. The difference is mu (1) - mu (2) and its estimate is 0.230000. The 95% lower bound for difference is -1.271079. The T-Test of difference: T-Value = 0.25, P- Value =0.400, DF=210. From the output we learn that: (i) 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. (ii) The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score. (iii) The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens. (iv) 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.

Step-by-step explanation:

Hello!

You have the output:

Two-Sample T-Test and Cl

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

This output summarizes the information of the two samples and indicates the order the populations where studied.

It also informs you of the value of the statistic under the null hypothesis and the p-value.

Unfortunately, there is no information on the type of hypotheses that were tested, i.e. if they where two-tailed or one-tailed, in the latter case, there is no information if it was left-tailed or right-tailed). Likewise is not specified if the test was done for a specific value of the parameter. (for example μ₁ - μ₂ = 0 or μ₁ - μ₂ = θ₀)

For these reasons, the data provided by the output isn't enough to conclude any hypothesis.

From all the provided answers the one more likely to be correct is:

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

I hope this helps!

iv

Step-by-step explanation:

Since the p-value (0.4) is greater than the significance level (0.05), we can conclude that the result is not significant. This means that there is no enough statistical evidence to reject the null hypothesis H0. Therefore, we must accept it and conclude that the mean depression score for male and female teens do not differ.

d. is the correct answer

step-by-step explanation: