Question

A new psychological treatment for depression is under investigation. Patients are given a psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% CI for the population average difference in test scores (before-after) is given by (.25, 3.75), which was computed based on a random sample of 36 patients. a. What is the hypothesis test to use? b. Is there a significant difference in test scores (before - after) on average? Perform an appropriate hypothesis test using ? = 0.10. I. State H0 and Ha. II. List data assumptions. III. Calculate the test statistic. IV. Specify rejection region for H0. Use appropriate distribution critical values. V. Make decision and conclusion.

          A new psychological treatment for depression is under investigation. Patients are given a psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% CI for the population average difference in test scores (before-after) is given by (.25, 3.75), which was computed based on a random sample of 36 patients.

a. What is the hypothesis test to use?
b. Is there a significant difference in test scores (before - after) on average? Perform an appropriate hypothesis test using ? = 0.10.
I. State H0 and Ha.
II. List data assumptions.
III. Calculate the test statistic.
IV. Specify rejection region for H0. Use appropriate distribution critical values.
V. Make decision and conclusion.

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A new psychological treatment for depression is under investigation. Patients are given a psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% CI for the population average difference in test scores (before-after) is given by (.25, 3.75), which was computed based on a random sample of 36 patients.

a. What is the hypothesis test to use?
b. Is there a significant difference in test scores (before - after) on average? Perform an appropriate hypothesis test using ? = 0.10.
I. State H0 and Ha.
II. List data assumptions.
III. Calculate the test statistic.
IV. Specify rejection region for H0. Use appropriate distribution critical values.
V. Make decision and conclusion.

Added by Santiago M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

09/07/2023

Step 1

State the null hypothesis (H0) and alternative hypothesis (Ha): H0: There is no significant difference in test scores before and after treatment, i.e., μd = 0 Ha: There is a significant difference in test scores before and after treatment, i.e., μd ≠ 0 II. List Show more…

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A new psychological treatment for depression is under investigation. Patients are given a psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% confidence interval for the population average difference in test scores (before - after) is given by (0.25, 3.75), which was computed based on a random sample of 36 patients. What is the hypothesis test to use? Is there a significant difference in test scores (before and after) on average? Perform an appropriate hypothesis test using α = 0.10. I. State H0 and Ha. II. List data assumptions. III. Calculate the test statistic. IV. Specify the rejection region for H0. Use appropriate distribution critical values. V. Make a decision and conclusion.

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Transcript

00:01 So we have a new psychological treatment for depression, and they found a before minus after.

00:06 We said that there are 36 patients, and they have a 95 % confidence interval for that difference, for that mean difference, being 0 .25 to 3 .75.

00:21 So doing that analysis, if we kind of break this out, we know that that difference, 3 .75, or we find the mean of those two, adding them together and dividing by 2, we'd find that the x bar had to have been 2.

00:37 And then they would have taken 2 plus or minus, and that margin of error would end up being 1 .75.

00:46 And since there were 36 numbers, that would have come from a t value.

00:50 And let's look what that t value is with 35 degrees of freedom.

00:55 And for 95%, that would have a 0 .025 in the upper tail.

01:01 So 0 .025 with 35 degrees of freedom would be a value of 2 .030, 2 .030.

01:13 And then there would be a certain standard deviation divided by that square root of 36.

01:18 And this value has to equal that 1 .75.

01:21 So the standard deviation has to be 1 .75 times 6 divided by 2 .030.

01:31 So i have that the standard deviation would be 5 .172.

01:36 Now, using that margin of error.

01:43 Now, you ask in part a, what's your null and alternative hypothesis? well, you'd be assuming that the mean difference is equal to 0.

01:55 And then alternately, it just asks if there is a difference.

01:59 So we would be doing a not equal to.

02:03 And then it asks you to list the data assumptions.

02:08 Well, our data assumptions are, let me go back to part b so i can read this better on a full sheet...

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