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Q2) Paired-Samples t Test A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from some elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at a = .05 for a one-tailed hypothesis test. Memory score Subject 1 2 3 4 5 6 7 8 9 10 Age 65 62 95 55 90 98 73 73 71 82 66 Age 75 65 88 56 89 90 75 70 70 80 62

Q2) Paired-Samples t Test A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from some elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at a = .05 for a one-tailed hypothesis test. Memory score Subject 1 2 3 4 5 6 7 8 9 10 Age 65 62 95 55 90 98 73 73 71 82 66 Age 75 65 88 56 89 90 75 70 70 80 62

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Q2) Paired-Samples t Test A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from some elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at a = .05 for a one-tailed hypothesis test. Memory score Subject 1 2 3 4 5 6 7 8 9 10 Age 65 62 95 55 90 98 73 73 71 82 66 Age 75 65 88 56 89 90 75 70 70 80 62
Transcribed Image Text:Q2) Paired-Samples t Test A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from some elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at a = .05 for a one-tailed hypothesis test. Memory score Subject 1 2 3 4 5 6 7 8 9 10 Age 65 62 95 55 90 98 73 73 71 82 66 Age 75 65 88 56 89 90 75 70 70 80 62
a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared). b. Explain why a paired-samples t test is appropriate for answering this research question. c. What would be the null and alternative hypotheses in both words and symbol notations? d. Calculate the difference score by subtracting each "Age 65" score from the associated "Age 75" score for each subject. Fill in the column in the table below for "difference score." Hint: The difference score is calculated as (age 75 minus age 65), so a negative number indicates a decline in memory performance, which is the researcher's hypothesis. Subject 1 2 3 4 5 6 7 8 9 10 Difference score (Age 75 minus Age 65) e. Calculate the mean and standard error from the sample of difference scores. f. Calculate the t statistic for the sample of difference scores. g. Determine the critical t value(s) based on the type of test, the preset alpha level, and degrees of freedom. h. Using jamovi, what is the corresponding p value for the t statistic? i. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Compare as well the p value with the alpha. Based on these comparisons, do we "reject" or "fail to reject" the null hypothesis? k. Interpret the result in 1 sentence to answer the research question. 1. Supporting Screenshot
Transcribed Image Text:a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared). b. Explain why a paired-samples t test is appropriate for answering this research question. c. What would be the null and alternative hypotheses in both words and symbol notations? d. Calculate the difference score by subtracting each "Age 65" score from the associated "Age 75" score for each subject. Fill in the column in the table below for "difference score." Hint: The difference score is calculated as (age 75 minus age 65), so a negative number indicates a decline in memory performance, which is the researcher's hypothesis. Subject 1 2 3 4 5 6 7 8 9 10 Difference score (Age 75 minus Age 65) e. Calculate the mean and standard error from the sample of difference scores. f. Calculate the t statistic for the sample of difference scores. g. Determine the critical t value(s) based on the type of test, the preset alpha level, and degrees of freedom. h. Using jamovi, what is the corresponding p value for the t statistic? i. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Compare as well the p value with the alpha. Based on these comparisons, do we "reject" or "fail to reject" the null hypothesis? k. Interpret the result in 1 sentence to answer the research question. 1. Supporting Screenshot
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