Question

Does our cognitive capacity change as we age? Researchers have noted a change in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggests that the antioxidants in foods such as blueberries may reduce and even reverse these age-related declines.

You decide to conduct your own study using a related-samples (within-subjects) design, to determine if a blueberry supplement can change cognitive capacity in older adults. You will use an alpha level = .05, and choose to examine 8 adults who are between the ages of 65 and 75 to measure their cognitive capacity using a standardized test. Cognitive capacity is measured at the beginning of the experiment (higher scores mean better cognitive capacity). Participants then begin a 2 month program in which they receive daily doses of a blueberry supplement. At the end of the 2 month period participants’ cognitive capacity is measured again using the same test.

Cognitive Capacity at start of experiment --   Cognitive Capacity after 2 months

P1 =73

P2 = 68

P3 = 59

P4 = 78

P5 = 75

P6 = 71

P7 = 80

P8 = 64

P1 = 75

P2 = 67

P3 = 73

P4 = 80

P5 = 75

P6 = 70

P7 = 87

P8 = 73

Basic information, compute a differential mean and standard deviation (thus, you should compute a sum of squares too!)1 point.

Step 1: What are your null and alternative hypotheses? (1 point)

Step 2: Alpha level is .05 and it’s a two tail test. What are your degrees of freedom? What is the t critical? (1 point)

Step 3: Obtain the test statistic: That is, what is your “obtained” value? - Begin by reporting the estimated population variance. (1 point) - Continue by computing the estimated standard error of the mean (1 point) - Finally, compute a t test. What is your obtained value? (1 point)

Step 4: Make your decision: Do you reject, or fail to reject the null hypothesis? What is your conclusion? (1 point) -

Based on your decision of step 4, would you compute effect size? If so, do it! (1 point) -

Of course, if you compute effect size you should report the percentage of variability (1 point)

Step 5: Write a formal interpretation of your results using statistical notations. (1 point)

Answer 1

Let the population mean difference be denoted by

Here we are to test

The given data are summarized as follows:

Sample size	n=8
Sample mean	=-4
Sample SD	s=5.451081

The df is given by 7. The critiical value of t is obtained as

The test statistic is given by

As the observed value is less than the critical value, we fail to reject the null hypothesis at 5% level of significance and hence conclude that there is no significant effect of the experiment.

The effect size is given by

Hence the effect size is 73.38%

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.