Question

A researcher tested a research hypothesis that people with diagnosed depression will have REDUCED level of depressive symptoms after a cognitive therapy treatment, as compared to the pre-treatment level of depressive symptoms. The cutoff t value is -1.833 for this one-tailed test. The data analysis yielded a mean change score (post-treatment minus pre-treatment) of -2.5. If the standard error is 2.0, what is the t statistic and what is the conclusion of the hypothesis test?

-2.5; fail to reject the null hypothesis

-1.25; reject the null hypothesis

-1.25; fail to reject the null hypothesis

-2.5; reject the null hypothesis

A researcher conducts a t test for dependent means (paired-samples t test) with 16 participants. The estimated population variance of the change scores is 9. What is the standard error?

1.5

.5625

.75

.1875

In a small-scale trial (sample size = 9) of a psychotherapy treatment for depression, participants were assessed with a depression scale when they entered the trial and again when they have completed the 6-month trial. The data yielded a mean difference (change) score of 1.5 and the standard deviation of the sampling distribution was .6. What was the the t statistic?

.5

1.5

2.5

.17

In a high school math class, there are 13 male students and 17 female students. After all the students have taken the ACT test, the math teacher would like to know if there is a significant difference in the math component score between the male and female students. If he uses an alpha level of .05 for a two-tailed test, what would be the critical t value for his statistical test?

±2.043

±2.049

± 2.120

± 1.701

Answer 1

Q1. Answer: Option B i.e., -1.25; reject the null hypothesis

Given,

Mean change score (post-treatment minus pre-treatment) = -2.5

Standard Error (S.E.) = 2.0

The t-statistic is given as below

.. (I)

Also given, the tabulated t cut-off value for this one-tailed test = -1.833 ...(II)

From (I) and (II), as the calculated t-statistic (= -1.25) > the tabulated t cut-off value (= -1.833) we infer that there is a significant difference between scores of post-treatment and pre-treatment i.e., people with diagnosed depression will have REDUCED level of depressive symptoms after a cognitive therapy treatment as compared to the pre-treatment level of depressive symptoms

Q2. Answer: Option C i.e., 0.75

Given, the sample size n = 16

Estimated population variance of the changed scores

The standard error (S.E.) is calculated as

Hence the standard error (S.E.) = 0.75

Q3. Answer: None of the options given. As the calculated t- statistic = 7.5

Given

Mean difference (change) score,  

Standard deviation of the sampling distribution,

Sample Size, n = 9

The t statistic is given below

Q4 Answer: Option B i.e., ±2.049

Given

Sample size of male students (n1) = 13

Sample size of female students (n2) = 17

Hence the critical t value to be observed for alpha = 0.05 is at 28 degrees of freedom (n1+n2-2 = 13+17-2 = 30 - 2 = 8), and the critical value for two-tailed test is given as