# MATHEMATICS

6. For which of the following situations is the **independent** groups t-test appropriate (if inappropriate, why?):

a. The independent variable is infant birth weight at one week (normal vs high); the dependent variable is resting heart rate.

b. The independent variable is radiation treatment on throat cancer patients (after a low dose and then a high dose treatment); the dependent variable is white blood cell count.

c. The IV is infant birth weight (low vs normal vs high); the DV is number of days absent from school in first grade.

d. The IV is gender (male vs female); the DV is compliance vs noncompliance with a medication regimen.

e. The independent variable is married status (single vs married); the dependent variable is happiness measured on a scale from 1 to 50

TIP:

Determine the characteristics of independent groups for t-tests? How many groups are there in the situation? Are there 2 groups in the situation? Are they independent groups and is the DV interval/ratio? If the answer is “yes” to the 3 questions, the situation is APPROPRIATE and you should state that it is so. If one or more of the conditions is/are not present, then the test is inappropriate.

7. For which of the following situations is the **dependent** groups t-test appropriate (if not appropriate, why?)

a. The IV is presence or absence of conversation directed to comatose patients (same patients with and without conversation); the DV is the patients’ intracranial pressure.

b. The IV is birth type (home vs hospital); the DV is perceived functional ability of the patient 48 hours after surgery.

c. The IV is time since incarceration (1 months vs 3 months vs 6 months); the DV is body weight.

d. The IV is menopausal state (pre vs post) in the same women over time; the DV is attitudes toward menopause.

e. The IV is nap therapy for narcoleptics (same patients before vs after treatment); the DV is the type of nap they had the following week (had unplanned vs didn’t have unplanned nap).

TIP: Determine the characteristics of dependent groups for t-tests. How many groups are there in the situation? Are there 2 groups in the situation? Are they dependent groups and is the DV interval/ratio? If the answer is “yes” to the 3 questions, the situation is APPROPRIATE and you should state that it is so. If one or more of the conditions is/are not present, then the test is inappropriate

8. 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). Use the following information. Compute a *t*-statistic for independent groups:

mean group 1 = 79.1 SD^{2}_{1} = 42.1 n_{1} = 25

mean group 2 = 74.1 SD^{2}_{2} = 39.7 n_{2 }= 25

What are the degrees of freedom and the value of* t* ? Using α=0.05 for a two-tailed test, is this *t* statistic significant? Show your calculations (or StatCrunch output) for full credit.

9. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 8.

TIP: For the report, please use the t-test value, the p-value from the test, state whether the result is significant or not and whether you would reject/accept the null hypothesis.

10. For each of the following t values, indicate whether the *t *is statistically significant for a two-tailed test, at the specified alphas:

a. *t* = 2.90, *df* = 25, α = 0.001

b. *t* = 2.00, *df* = 25, α = 0.05

c. *t *= 5.52, *df *= 10, α = 0.01

d. *t *= 2.02, *df *= 20, α = 0.05

* *

TIP: Use the tables on page 412 to obtain your answer. If the t-value is GREATER than the value in the critical/tabled value, the result is statistically significant.

* *

11. For each of the following situations, indicate whether ANOVA is appropriate; if not appropriate, the reason why not; and, if appropriate, the type of ANOVA that would be used (i.e., one-way, repeated measures, etc.)

a. The IVs are ethnicity (Asian, White, African American, Hispanic) and gender (male vs female); the DV is serum cholesterol levels.

b. The IV is smoking status – smokers vs non-smokers; the DV is health-related hardiness as measured on a 20-item scale.

c. The IV is maternal breast feeding status (breastfeeds daily vs breastfeeds at least 1-3 times/week vs doesn’t breastfeed); the DV is maternal bonding with infant, as measured on a 20-item self-report scale.

d. The IV is treatment group for patients with drug-induced shivering (extremity wraps vs high room temp vs normal room temp without wraps) different patients used for each treatment; the DV is myocardial oxygen consumption (measured in ml O_{2}/min per 100g of tissue).

e. The IV is length of gestation (preterm vs term vs postterm) using the same multiple birth mothers over time; the DV is blood pressure 10 minutes post delivery.

TIP: Determine the characteristics of ANOVAs. How many groups are there in the situation? Are there 3 groups in the situation? Is the DV interval/ratio? If the answer is “yes” to all the questions, the situation is APPROPRIATE and you should state that it is so. If one or more of the conditions is/are not present, then the test is inappropriate. If it is APPROPRIATE, please state which type of ANOVA it is.