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- From: Mathematics, Statistics and Probability
- Posted on: Tue 19 Jan, 2016
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1. What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)? What is the probability that a player can roll a four 3 times in a row (assume that rolling the dice each time does not affect the outcome of the next roll)?
2. Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why?
3. Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 50 patients. The mean vein size is found to be 7.8mm with an SD of 2.1. Using the t distribution, what are the confidence limits for a 95% confidence interval? For a 99% confidence interval?
4. In a pilot study evaluating the use of a new drug to lower resting heart rates (HR) of patients, the following data was recorded:
Given that the average resting HR of the general population for this study is 72, use StatCrunch to perform the appropriate t test. What is the value of t? Using an alpha of 0.05, is the t statistic significant? Why? What are the confidence limits for a 95% confidence interval here and what do they mean for this patient group? Copy and Paste your work from StatCrunch into your Word document submission.
4. Be sure to clearly state the hypotheses and a meaningful conclusion.
5. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise
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 birth weight); 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 divorced vs married); the dependent variable is happiness measured on a scale from 1 to 50
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); 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).
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 = 78.1 SD21 = 42.1 n1 = 25
mean group 2 = 75.1 SD22 = 39.7 n2=25
What are the degrees of freedom and the value of t ? Using ?=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. Be sure to clearly state the hypotheses and a meaningful conclusion.
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, ? = 0.01
b. t = 2.00, df = 25, ? = 0.05
c. t = 5.52, df = 10, ? = 0.01
d. t = 2.02, df = 150, ? = 0.05
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) same patient used for each treatment; the DV is myocardial oxygen consumption, measured before and after treatment.
e. The IV is length of gestation (preterm vs term vs postterm); the DV is delivery type (vaginal vs Caesarean).
12. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking. Using the following data for PSS, do a one-way ANOVA to test the hypothesis that the population means are equal:
Nonsmokers Smokers Quitters
19 31 30
28 29 22
17 22 23
20 24 22
25 19 17
Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission.
13. A new motorcycle is being developed to meet new gas mileage standards recently passed by the federal government. An engineer tested three model designs by randomly assigning the motorcycles in a blind study (the riders recorded the mileage but did not know the design of the motorcycle, only its code). The data in miles per gallon (MPG) for the three designs is listed below:
Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What are the hypotheses to be tested here? What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission for full credit.
14. For each of the following F values, indicate whether the F is statistically significant at the specified alpha level:
a. F = 4.80, df = 4, 40 ? = 0.01
b. F = 5.02, df = 3, 60, ? = 0.001
c. F = 3.45, df = 3, 27, ? = 0.05
d. F = 4.99, df = 2, 150, ? = 0.01
e. F = 2.09, df = 2, 250, ? = 0.05
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