The following sample of n6 scores was obtained from a popula

The following sample of n=6 scores was obtained from a population with unknown parameters.

Scores: 5, 5, 3, 4, 6, 7

            a.         Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.)

            b.         Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)

AND

Oishi and Shigehiro (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n=12 young adults who each experienced 5 or more different homes before they were 16 years old. These participants were given a standardized well-being questionnaire for which the general population has an average score of µ=35. The well-being scores for this sample are as follows: 33, 32, 36, 30, 37, 35, 28, 28, 31, 33, 27, 34.

            a)         On the basis of this sample, is well-being for frequent movers significantly different from well-being in the general population? Use a two-tailed test with =.01.

            b)         Compute the estimated Cohen’s d to measure the size of the difference.

Solution

a) mean = 5, s.d = 1.414214.........

b) the estimated standard error for M = 1.414214 / sqrt(6) = 0.57735......

2) poulation mean = 35....

sample mean= 32..sample s.d = 3.275252....

Standard error = 3.275252 / sqrt(12) = 0.9454838

Test statistic = 32 - 35 / 0.9454838 = -3.172979...
p-value= 0.004435707

so, at 0.01 level...we reject our null hypothesis and we can say that well-being for frequent movers is significantly different from well-being in the general population...

(b)

Cohen\'s d = 2t /(df)

r_Yl = (t² / (t² + df))

so, d= -2.00676812 and r = 0.7083002