Five people, who were suffering from depression, attended 10 one-hour counseling sessions. The following table gives the depression scores (on a scale of 1 to 10) of these five people before and after attending the counseling sessions. Note that a higher score means that a person has a worse case of depression. Before After 7.5 4.3 6.4 5.1 7.1 6.2 9.7 6.9 7.8 7.2 The null hypothesis is the mean of the population paired differences is equal to zero (i.e., attending the counseling sessions does not change the depression score). The alternative hypothesis is that the mean of the population paired differences is not equal to zero (i.e., attending the counseling sessions does change the depression score). The significance level is 5%. 4.1. By hand, what is the mean of the sample paired differences (d), rounded to two decimal places? 4.2. What is the standard deviation of the paired differences (oa) , rounded to three decimal places? 4.3. By hand, what is the standard deviation of the mean of the sample paired differences (sa), rounded to three decimal places?

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Five people, who were suffering from depression, attended 10 one-hour counseling sessions. The
following table gives the depression scores (on a scale of 1 to 10) of these five people before and
after attending the counseling sessions. Note that a higher score means that a person has a worse
case of depression.
Before
After
7.5
4.3
6.4
5.1
7.1
6.2
9.7
6.9
7.8
7.2
The null hypothesis is the mean of the population paired differences is equal to zero (i.e.,
attending the counseling sessions does not change the depression score). The alternative
hypothesis is that the mean of the population paired differences is not equal to zero (i.e.,
attending the counseling sessions does change the depression score). The significance level is
5%.
4.1. By hand, what is the mean of the sample paired differences (d), rounded to two decimal
places?
4.2. What is the standard deviation of the paired differences (o4) , rounded to three decimal
places?
4.3. By hand, what is the standard deviation of the mean of the sample paired differences (sa),
rounded to three decimal places?
4.4. Calculate the 95% confidence interval for the mean of the population paired differences that
corresponds to these data, rounded to two decimal places.
4.5. What is/are the critical value(s) for the hypothesis test?
4.6. What is the value of the test statistic, rounded to three decimal places?
4.7. What is the p-value for this test, rounded to four decimal places?
4.8. Using both the p-value and critical value approaches, do you reject or fail to reject the null
hypothesis?
Transcribed Image Text:Five people, who were suffering from depression, attended 10 one-hour counseling sessions. The following table gives the depression scores (on a scale of 1 to 10) of these five people before and after attending the counseling sessions. Note that a higher score means that a person has a worse case of depression. Before After 7.5 4.3 6.4 5.1 7.1 6.2 9.7 6.9 7.8 7.2 The null hypothesis is the mean of the population paired differences is equal to zero (i.e., attending the counseling sessions does not change the depression score). The alternative hypothesis is that the mean of the population paired differences is not equal to zero (i.e., attending the counseling sessions does change the depression score). The significance level is 5%. 4.1. By hand, what is the mean of the sample paired differences (d), rounded to two decimal places? 4.2. What is the standard deviation of the paired differences (o4) , rounded to three decimal places? 4.3. By hand, what is the standard deviation of the mean of the sample paired differences (sa), rounded to three decimal places? 4.4. Calculate the 95% confidence interval for the mean of the population paired differences that corresponds to these data, rounded to two decimal places. 4.5. What is/are the critical value(s) for the hypothesis test? 4.6. What is the value of the test statistic, rounded to three decimal places? 4.7. What is the p-value for this test, rounded to four decimal places? 4.8. Using both the p-value and critical value approaches, do you reject or fail to reject the null hypothesis?
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