Question

Oishi and Schimmack (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 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 . The well-being scores for this sample are as follows: 38, 37, 41, 35, 42, 40, 33, 33, 36, 38, 32, 39. 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 . Compute the estimated Cohen’s d to measure the size of the difference. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

Answer 1

Answer:

The well-being for frequent movers is significantly different from well-being in the general population. ( Alternate Hypothesis accepted )

cohen's d = -0.91 , ( Large Effect )

Step-by-step explanation:

Given:-

- A sample of size n = 12

- The population mean u_p = 40

- The sample was taken as:

                     38, 37, 41, 35, 42, 40, 33, 33, 36, 38, 32, 39

Find:-

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 α = 0.05.

Solution:-

- State the hypothesis for sample mean u_s is same as population mean u_p.

                    Null Hypothesis: u_s = 40

                    Alternate Hypothesis: u_s ≠ 40

- The rejection criteria for the Null hypothesis can be modeled by T-value ( n < 30 ) with significance level α = 0.05.

                    DOF = n - 1 = 12 - 1 = 11

                    Significance level α = 0.05

                    t_α/2 = t_0.025 = +/- 2.201

- For the statistic value we have to compute sample mean u_s given by:

             u_s = Σ xi / n

             u_s = (38 + 37 + 41 + 35 + 42 + 40 + 33 + 33 + 36 + 38 + 32 + 39) / 12

             u_s = 37

- For the statistic value we need population standard deviation S_p given by:

            S_p = S_s / √n

Where, S_s : Sample standard deviation.

            S_s^2 = Σ (xi - u_s)^2 / (n-1)

            =[ 2*(38-37)^2 +  (37-37)^2 + (41-37)^2 + (35-37)^2 + (42-37)^2 + (40-37)^2 + 2*(33-37)^2 + (36-37)^2 + (32-37)^2 + (39-37)^2 ] / ( 11 )

            S_s^2 = [ 2 + 0 + 16 + 4 + 25 + 9 + 32 + 1 + 25 + 4 ] / 11

            S_s^2 = 10.73

            S_s = 3.28

The population standard deviation ( S_p ) is:

            S_p = 3.28 / √12

            S_p = 0.95

- The T-statistics value is computed as follows:

            t = ( u_s - u_p ) / S_p

            t = ( 37 - 40 ) / 0.95 = -3.16

- Compare the T-statistics (t) with rejection criteria (t_α/2).

            -3.16 < -2.201

            t < t_α/2 ...... Reject Null Hypothesis.

- The well-being for frequent movers is significantly different from well-being in the general population. ( Alternate Hypothesis accepted )

- The cohen's d is calculated as follows:

         cohen's d = ( u_s - u_p ) / S_s

         cohen's d = ( 37 - 40 ) / 3.28 = -0.91 ,     ( Large Effect )