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Five persons, 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 persons before and after attending the counseling sessions. Note that a higher score means that a person has a worse case of depression.
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Before |
After |
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7.5 |
4.3 |
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6.4 |
5.1 |
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7.0 |
6.2 |
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9.2 |
6.9 |
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7.8 |
7.2 |
Let the paired difference be the score before minus the score after attending the counseling sessions. The null hypothesis is that the mean of the population paired differences is equal to zero (i.e. Attending the counseling sessions does not change 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%.
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20. |
What is the mean of the sample paired differences, rounded to two decimal places? 1.92 |
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21. |
What is the standard deviation of the paired differences, rounded to three decimal places?
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22. |
What is the standard deviation of the mean of the sample paired differences, rounded to three decimal places? |
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23. |
Calculate the 95% confidence interval for the mean of the population paired differences that corresponds to these data, rounded to two decimal places.
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24. |
What are the critical values of t for the hypothesis test? |
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A) |
-2.776 and 2.776 |
C) |
-2.132 and 2.132 |
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B) |
-2.571 and 2.571 |
D) |
-2.015 and 2.015 |
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25. |
What is the value of the test statistic, t, rounded to three decimal places?
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26. |
What is the p-value for this test, rounded to four decimal places?
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27. |
Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject", but don't include the quotation marks.
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