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Statistics Question

Statistics Question

Question Description

I’m working on a statistics practice test / quiz and need support to help me study.

QUESTION 1

  1. A study by Professor Brian Everitt (Institute of Psychiatry, London) compared therapies for teenage girls suffering from anorexia, an eating disorder that can cause dangerously low weight. Girls were assigned to a control group and two different treatment groups. In the “cognitive behavioral therapy” treatment, the emphasis was on identifying the thinking that causes undesirable behavior, and replacing it with thoughts designed to improve behavior. The data you will work with are the weight before treatment and weight after treatment for 29 girls in the cognitive behavioral therapy treatment group.A data file anorexia-cognitive-behavioral-wide.csv has two columns: the first column has weight before treatment (cog1), i.e., at time 1, and the second column has weight after treatment (cog2), i.e., at time 2. Another data file anorexia-cognitive-behavioral-tall.csv, has one column for each girl’s weight and another indicating whether the measure was from before treatment (time = 1) or after treatment (time= 2).anorexia-cognitive-behavioral-wide.csv anorexia-cognitive-behavioral-tall.csv Begin by calculating the average weight before treatment for girls in the cognitive behavioral therapy group. Use three decimal points.

5 points

QUESTION 2

  1. Calculate the standard deviation of weight before treatment for girls in the cognitive behavioral therapy group. Use three decimal points.

5 points

QUESTION 3

  1. Calculate the average weight after treatment for girls in the cognitive behavioral therapy group. Use three decimal points.

5 points

QUESTION 4

  1. Calculate the standard deviation of weight after treatment for girls in the cognitive behavioral therapy group. Use three decimal points.

5 points

QUESTION 5

  1. Calculate the difference of means from before to after therapy. Your answer should be a positive number. Use three decimal points.

5 points

QUESTION 6

  1. Calculate the standard error of the difference of means using either estimator. Because the sample sizes are equal (which they must be, since these are dependent samples) both equations will yield the same answers. Use three decimal points.

5 points

QUESTION 7

  1. Calculate the “difference of means” t statistic, against the null hypothesis that the difference between the population means equals zero. Use three decimal points.

5 points

QUESTION 8

  1. If you used the pooled estimator, how many degrees of freedom would you have for finding the t * critical value in the t Table?

5 points

QUESTION 9

  1. Using your answer to question 8, find the t* critical value at the 95% confidence level. Round to two decimal points.

5 points

QUESTION 10

  1. Compare the t statistic against the t * critical value. True or false: on the basis of this sample, I would retain the null hypothesis of no difference.

5 points

QUESTION 11

  1. How would you interpret the results of this study? Choose the best answer.
    Cognitive behavioral therapy leads to weight reduction for girls who were dealing with anorexia, and the difference is statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight increases for girls who were dealing with anorexia, and the difference is statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight reduction for girls who were dealing with anorexia, but the difference is not statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight increases for girls who were dealing with anorexia, but the difference is not statistically significant at the 95% confidence level.

5 points

QUESTION 12

  1. Use the data file anorexia-cognitive-behavioral-wide.csv to calculate the deltas for all 29 girls, the average delta (which should equal the difference of means) and the standard deviation of the deltas. What is the standard deviation of the deltas? Use three decimal points.

5 points

QUESTION 13

  1. What is the standard error of the mean delta? Remember to divide by the square root of the number of pairs. Use three decimal points.

5 points

QUESTION 14

  1. What is the “mean of differences” t statistic? Round to two decimal points.

5 points

QUESTION 15

  1. How many degrees of freedom do you have for the mean of differences t test?

5 points

QUESTION 16

  1. What is the t* critical value for the degrees of freedom equal given in problem 24, at the 95% confidence level? Use two decimal points.

5 points

QUESTION 17

  1. Compare the t statistic in 23 against the t * critical value in 25. True or false: on the basis of a mean of differences t test, I would retain the null hypothesis of no difference.

5 points

QUESTION 18

  1. How would you interpret the results of this study? Choose the best answer.
    Cognitive behavioral therapy leads to weight reduction for girls who were dealing with anorexia, and the difference is statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight increases for girls who were dealing with anorexia, and the difference is statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight reduction for girls who were dealing with anorexia, but the difference is not statistically significant at the 95% confidence level.
    Cognitive behavioral therapy leads to weight increases for girls who were dealing with anorexia, but the difference is not statistically significant at the 95% confidence level.

5 points

QUESTION 19

  1. It turns out that the correlation between weight before and weight after is r = 0.492. Use the equation in lecture 3 to find the corrected standard error of the difference of means.

5 points

QUESTION 20

  1. True or false: Panel studies have desirable properties in terms of statistical inference and sometimes yield different conclusions and interpretations than we would reach if we treated data as coming from independent samples.

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