Worked Problem.....Correlated t test.....Psyc205/Soc205.....Vernoy

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t Test for Correlated Samples
(A worked Problem: Procedure explained in more detail in Chapter 12)

Some investigators have proposed that students have elevated blood pressure during finals week. To test this hypothesis 8 students volunteered to have their blood pressure taken at the beginning of the semester and then again during finals week. The blood pressure data (diastolic) is listed below. Conduct a t test to determine if there is a difference between the first week and finals week.

Student	Week 1	Finals Week
Rod	89	92
William	76	78
Barbara	84	92
Marvin	89	94
Dennis	74	93
Karen	66	74
Mora	56	65
Michael	74	73

I. Because we have two correlated samples we will conduct a t test for correlated samples.

II. State the hypotheses

A. Null Hypothesis

B. Research Hypothesis

III. Compute the standard error of the difference using the difference method

A. Compute the differences (D)

Student	Week 1	Finals Week	D
Rod	89	92	-3
William	76	78	-2
Barbara	84	92	-8
Marvin	89	94	-5
Dennis	74	93	-19
Karen	66	74	-8
Mora	56	65	-9
Michael	74	73	1
Total			-53

B. Compute the mean of the differences

Note: n = the number of pairs

C. Square the differences

Student	Week 1	Finals Week	D	D²
Rod	89	92	-3	9
William	76	78	-2	4
Barbara	84	92	-8	64
Marvin	89	94	-5	25
Dennis	74	93	-19	361
Karen	66	74	-8	64
Mora	56	65	-9	81
Michael	74	73	1	1
Total			-53	609

D. Compute the standard error of the difference

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IV. Compute t

V. The significance of t

A. Compute the degrees of freedom

df = n - 1 = 8 - 1 = 7

Note: n = the number of pairs

B. Look up the critical value in Table T using the column for a one-tailed research hypothesis

C. V. = 1.895

    C. Conculusion: because the computed t, 3.087, is greater than the critical value, 1.895,
            we can reject H_o and accept H₁. Therefore students have significantly higher
            blood pressure during finals week than they do during the first week of the semester.