A clinician interested in agoraphobia (fear of public places) tests a new treatment method. She samples five agoraphobics from her clinic and has them report how many times they ventured out of their houses (on their own) in the past month. They then received relaxation training and were introduced to trips away from their homes at gradually increasing durations. After 2 months, subjects again reported how many times they ventured (on their own) out of their houses. The data are below. Assess whether there is a significant change in trips outside the home from before to after therapy.a. What are the null and alternative hypotheses?b. What inferential test did you use? Using an alpha level of .05, determine whether the sample was significantly different from population. SubjectTrips beforeTrips after1223447526.3.3.

Name: A clinician interested in agoraphobia (fear of public places) tests a
Uploaded: 2024-03-20T07:06:27.000Z
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Description: A clinician interested in agoraphobia (fear of public places) tests a new treatment method. She samples five agoraphobics from her clinic and has them report how many times they ventured out of their houses (on their own) in the past month. They then

Given Information : A clinician interested in agoraphobia (fear of public places) tests a new treatment method. She samples five agoraphobics from her clinic and has them report how many times they ventured out of their houses (on their own) in the past month. They then received relaxation training and were introduced to trips away from their homes at gradually increasing durations. After 2 months, subjects again reported how many times they ventured (on their own) out of their houses. The data are provided. The question is whether there is a significant change in trips outside the home from before to after therapy. The following table is obtained: Trips before Trips after Difference 0 2 -2 0 2 -2 3 4 -1 3 7 -4 2 6 -4 Average 1.6 4.2 -2.6 St. Dev. 1.517 2.28 1.342 n 5 5 5 From the sample data, it is found that the corresponding sample means are: Also, the obtained sample standard deviations are: and the sample size is n = 5. For the score differences we have , Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: There is a no change in trips outside the home from before to after therapy. i.e. μD = 0 Ha: There is a significant change in trips outside the home from before to after therapy. i.e. μD ≠ 0 This corresponds to a two-tailed test, for which a t-test for two paired samples be used.Rejection Region Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the degrees of freedom are df = 4df=4. Hence, it is found that the critical value for this two-tailed test is t_c = 2.776tc=2.776, for \alpha = 0.05α=0.05 and df = 4df=4. The rejection region for this two-tailed test is R = \{t: |t| > 2.776\}R={t:∣t∣>2.776}. Test Statistics The t-statistic is computed as shown in the following formula: Decision about the null hypothesis Since it is observed that |t| = 4.333 > t_c = 2.776∣t∣=4.333>tc=2.776, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p=0.0123, and since p = 0.0123 < 0.05p=0.0123<0.05, it is concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that there is a significant change in trips outside the home from before to after therapy., at the 0.05 significance level.