# Compute the t statistic for dependent groups and the df for these data. Using α = .05 for a two-tailed test, is this t statistically significant? Attach SPSS printout.

1 For which of the following situations is the independent groups t-test appropriate (if inappropriate, indicate why):
a) The independent variable (IV) is type of stimulation for premature infants (auditory vs. visual vs. tactile); the dependent variable (DV) is cardiac responsiveness.
o Inappropriate because there are three groups, not two.
b) The IV is parental role within couples (mother versus father); the DV is degree of bonding with the infant.
o Inappropriate because the dependent groups t test should be used due to the pairing of the parents.
c) The IV is infant birthweight (low birthweight vs. normal birthweight); the DV is number of days absent from school in first grade.
o Appropriate.
d) The IV is sex (men vs. women); the DV is compliance vs. noncompliance with a medication regimen.
o Inappropriate because the dependent variable is measured on the nominal scale.
e) The IV is radiation treatments (before vs. after treatment); the DV is cancer patients’ perceived self-efficacy.
o Inappropriate because the dependent group t test should be used due to the similarities of people in both groups.

2 For which of the following situations is the dependent groups t-test appropriate (if inappropriate, indicate why):
a) The independent variable (IV) is presence or absence of conversation directed to comatose patients; the dependent variable (DV) is the patients’ intracranial pressure.
o Appropriate.
b) The IV is role (patient vs. nurse); the DV is perceived functional ability of the patient 48 hours after surgery.
o Appropriate.
c) The IV is time since incarceration (1 month vs. 3 months vs. 6 months); the DV is body weight.
o Inappropriate because there are three time periods instead of two.
d) The IV is age group (teenagers vs. young adults); the DV is attitudes toward condom use.
o Appropriate
e) The IV is nap therapy for narcoleptics (before vs. after treatment); the DV is unplanned naps the following week (had vs. did not have an unplanned nap).
o Inappropriate because the dependent variable is measured on the nominal scale.

3 Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Using the following information, the computed t statistic for independent groups is t=3.54:
M1 = 78.5 SD12 = 42.1 n1 =25
M2 = 72.1 SD22 = 39.7 n2 =25

a) What are the degrees of freedom? 48.
b) Using α = .05 for a two-tailed test, is this t statistically significant?
a. The value of t = 3.54. Using a 0.05, this value is statistically significant.
c) Write one or two sentences that could be used to report the results obtained for the t-test in question A3.
a. The results obtained during the t test were appropriate because the samples were independent giving a significant result.

4 For question 3, assume that the pooled SD for the two groups is 7.05. Calculate the value of d. Would you say the effective size is large, medium, or small?
o d= 0.91. I would say it is large.

5 For each of the following t values, indicate whether the t is statistically significant for a two-tailed test, at the specified alpha:

a. t = 2.40, df = 25, α = .01- NO
b. t = 2.40, df = 25, α = .05 – YES
c. t = 5.52, df = 10, α = .01 – YES
d. t = 2.02, df = 150, α= .05 – YES

6 State the critical (tabled) value of t that would be used to reject the null hypothesis of equality of population means, for an independent groups t-test under each of the following conditions:
a. H1: μ1 ≠ μ2; n1 = 20, n2 = 20; α = .05
b. H1: μ1 > μ2; n1 = 30, n2 = 30; α = .01
c. H1: μ1 ≠ μ2; n1 = 10, n2 = 10; α = .01
d. H1: μ1 > μ2; n1 = 60, n2 = 60; α = .05
e. H1: μ1 ≠ μ2; n1 = 15, n2 = 10; α = .01

7 For a post hoc power analysis, d = .60, α = .05 for a two-tailed t test, and the number of people in each of two groups = 30, the power of the t-test is approximately 0.61.
a. What was the risk of a Type II error?
b. For the same effect size (.60), approximately what n per group would be needed to achieve power = .80?

8 The following are data for subcutaneous oxygen tension (PSCO2, measured in mm Hg) 12 hours after the start of two protocols, administered to the same 10 healthy subjects in random order–a bed rest protocol and a high activity protocol:

Subject Bed Rest High Activity
1 67 63
2 68 62
3 70 69
4 66 64
5 68 67
6 62 60
7 71 66
8 65 65
9 67 63
10 65 62

Compute the t statistic for dependent groups and the df for these data. Using α = .05
for a two-tailed test, is this t statistically significant? Attach SPSS printout.

9 Suppose we wanted to test the hypothesis that the employment status of these disadvantaged women (i.e., whether they were working or not working at the time of the interview) was related to their level of depression.

(a) Formally state the null and alternative hypothesis for this situation.
(b) Would a dependent or independent t test be appropriate? Why?

10 Now run a t test to test the hypothesis, using the dataset “Statistics Polit SetC data.sav”: Analyze→ Compare Means→ Independent Samples T Test. Move the variable cesd (variable #35) into the slot for Test Variable(s). Then move the variable worknow (variable #6) into the slot for Grouping Variable. To run this analysis, you must know how the group variable is coded. For worknow, a code of 0 indicates that the woman was not working, and a code of 1 was used to code those who were employed. Click the “Define Groups” pushbutton and on the next dialog box enter 0 for Group 1 and 1 for Group 2. Then click Continue. Click the “Options” pushbutton and make sure that the computer will compute a 95% CI. Then click Continue and OK to run the analysis, and answer these questions:
a. How many women were employed versus not employed in this sample?
b. What are the mean CES-D scores for employed and non-employed women?
c. What is the value of the F statistic for Levene’s test, and what is the level of significance? What does this mean?
d. Which formula for t is appropriate in this situation – the pooled variance (equal variance assumed) or separate variance formula (equal variance not assumed)? Why?
e. What is the value of t for the appropriate test? What is the level of significance?
f. What is your conclusion? Is your research hypothesis supported? Write a paragraph reporting the result.
g. Attach the SPSS printout.

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