A study compared different psychological therapies for teenage girls suffering from anorexia, an eating disorder that causes them to become dangerously underweight. Each girl’s weight was measured before and after a period of therapy. The variable of interest was the weight change, defined as weight at the end of the study minus weight at the beginning of the study. Two therapies were designed to aid weight gain, one of which is the cognitive behavioral therapy. This form of psychotherapy stresses identifying the thinking that causes the undesirable behavior and replacing it with thoughts designed to help improve this behavior. The changes of 29 teenage girls receiving the cognitive behavioral therapy in weight (in lbs) during the study were 1.7, 11.7, -1.4, 0.7, 6.1, -0.8, -0.1, 1.1, 2.4, -0.7, -4.0, 12.6, -3.5, 20.9, 1.9, 14.9, -9.3, 3.9, 3.5, 2.1, 0.1, 17.1, 1.4, 15.4, -7.6, -0.3, -0.7,1.6, -3.7 The weight change was positive if the girl gained weight (which is desired) and negative if she lost weight. We want to test whether the cognitive behavioral therapy is effective to aid weight gain. (a) Formulate the null and alternative hypotheses for testing whether teenage girls receiving the cognitive behavioral therapy have a positive mean weight gain. (b) Calculate the t-statistic and report the degrees of freedom and find (a range for) the p-value and make a conclusion use a significance level of 0.01. (c) What are the Type 1 error and Type 2 error respectively for the hypothesis test done in part (a-b)?
A study compared different psychological therapies for teenage girls suffering from anorexia, an eating disorder that causes them to become dangerously underweight.
Each girl’s weight was measured before and after a period of therapy. The variable of interest was the weight change, defined as weight at the end of the study minus weight at the beginning of the study.
Two therapies were designed to aid weight gain, one of which is the cognitive behavioral therapy. This form of psychotherapy stresses identifying the thinking that causes the undesirable behavior and replacing it with thoughts designed to help improve this behavior. The changes of 29 teenage girls receiving the
cognitive behavioral therapy in weight (in lbs) during the study were
1.7, 11.7, -1.4, 0.7, 6.1, -0.8, -0.1, 1.1, 2.4, -0.7, -4.0, 12.6, -3.5, 20.9,
1.9, 14.9, -9.3, 3.9, 3.5, 2.1, 0.1, 17.1, 1.4, 15.4, -7.6, -0.3, -0.7,1.6, -3.7
The weight change was positive if the girl gained weight (which is desired) and negative if she lost weight.
We want to test whether the cognitive behavioral therapy is effective to aid weight gain.
(a) Formulate the null and alternative hypotheses for testing whether teenage girls receiving the cognitive behavioral therapy have a positive
(b) Calculate the t-statistic and report the degrees of freedom and find (a
(c) What are the Type 1 error and Type 2 error respectively for the hypothesis test done in part (a-b)?
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