Question

           Conduct hypothesis tests on the following question:

A researcher knows that the mean number of symptoms (e.g., fatigue, sleep disturbance, feelings of worthlessness, etc.) exhibited by the population of people with unipolar depression, prior to diagnosis, is 9.5. She suspects that being told that you suffer from unipolar depression increases that number. She randomly selects 14 individuals already with the diagnosis of unipolar depression and counts the number of symptoms they exhibit. The number of depressive symptoms exhibited by the 14 participants was:

   8, 9, 15, 19, 2, 8, 16, 14, 12, 13, 4, 15, 9, 10

         Does her hypothesis carry any weight at the .05 level?

Answer 1

H0: Null Hypothesis: 9.5

HA: Alternative Hypothesis: > 9.5

From the given data, the following statistics are calculated:

n = 14

= 154/14 = 11

s = 4.7394

SE=s/

= 4.7394/ = 1.2666

Test statistic is:

t = ( - )/SE

= (11 - 9.5)/1.2666 = 1.1843

= 0.05

ndf = 14 - 1 = 13

One tail - right side test

From Table, critical value of t = 1.7709

Since the calculated value of t = 1.1843 is less than critical value of t = 1.7709, Fail to reject H0.

Conclusion:

The data do not support the claim that being told that you suffer from unipolar depression increases that number.