Question

A researcher wants to compare the levels of recall in younger and older subjects. Her hypothesis is that if subjects are required to process verbal information (lists of words) older subjects do less processing and therefore will recall fewer words. The following data are from a group of older subjects and a group of younger subjects who were told to memorize the words presented to them so they could be recalled at a later time. The dependent variable is the number of correctly recalled items. Do these data indicate a significant difference in items recalled between younger and older adults? Use two-tailed α = .05. DATA: Younger adults: 23, 20, 16, 17, 21, 20, 20, 22, 10, 22 SS=44 M= 20. Older adults: 10, 19, 14, 5, 10, 11, 14, 15, 11, 11 SS= 126 M= 12

Answer 1

SD of younger adults = Sqrt(44/9) = 2.211

SD of Older adults = Sqrt(126/9) = 3.742

Since s₁/s₂ = 2.211/3.742 = 0.59 (it lies between 0.5 and 2) we used the pooled variance.

The degrees of freedom used is n1 + n2 - 2 = 10 + 10 - 2 = 18 (since pooled variance is used)

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The Hypothesis:

This is a Two tailed test.

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The Test Statistic:We use the students t test as population standard deviations are unknown.

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The p Value:    The p value (2 Tail) for t = 5.82, df = 18, is; p value = 0.0000

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The Critical Value:   The critical value (2 tail) at = 0.05, df = 18, tcritical = +2.1 and -2.1

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The Decision Rule: If tobservedis >tcriticalor If tobserved is < -tcritical, Then Reject H0.

Also If the P value is < , Then Reject H0

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The Decision:    Since t observed (5.82) is > tcritical (2.1), We Reject H0.

Also since P value (0.0000) is < (0.05), We Reject H0.

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The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a significant difference in items recalled between younger and older adults.

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