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Examples of Probability, Statistics and Medical Research Questions

## Question 1: Rolling a Die

1.What is the probability of rolling a four with a six sided die?  What is the probability that a person can roll a four 3 times in a row? (assume that rolling the die 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 50 people is picked from population A, and random sample of 20 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 4.7mm with an SD of 1.1.  Using a t distribution table and/or StatCrunch, 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:

 Subject # Resting HR 001 72 002 88 003 71 004 87 005 64 006 77 007 79 008 59 009 77 010 68 011 78 012 80 013 91 014 81 015 65 016 75 017 69

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.

5.Write a few sentences that could be used to report the results obtained for the t-test in Exercise 4.

6.A study by the Fellows Research Group evaluated the mental health status of 150 women in the inner city of Philadelphia.  The results of the study are in an Excel file in the Week 2 assignment area and in the “Course Resources” area.  Load the data set into StatCrunch and perform a one sample t test on the mental health score given that the national average on this test is 45. Is the result significant?  Copy and paste your StatCrunch output into your submission document for full credit.

7.Write a few sentences that could be used to report the results obtained for the t-test in Exercise 6.

8.Looking again at the Fellows Research Group data used in exercise 6 above, perform a two-sample t test on the mental health score of the married and divorced subjects. Is the result significant?  What hypothesis did you test? Copy and paste your StatCrunch output into your submission document for full credit.

## Question 2: Estimating population means

9.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 (one group getting a low dose and the other a high dose treatment); the dependent variable is white blood cell count.

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

d.The IV is marital status (single vs divorced vs married); the DV is a happiness score, based on a 50 point scale.

10.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 on a 20 point scale 48 hours after surgery.

c.The IV is time since incarceration for a single group of ex-cons (measured at 1 months and 6 months); the DV is body weight.

d.The IV is menopausal state (pre vs during vs post) in the same women over time; the DV is attitudes toward menopause (measured in a survey score 1-20).

11.Suppose we wanted to test the idea 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 (variance) = 49.1 n1 = 25

mean group 2 = 74.1 SD22 (variance) = 59.7 n2 = 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.

12. For each of the following t values (a-d), indicate whether the t statistic is statistically significant for a two-tailed test, at the specified alphas:

a.t = 2.90, df = 25, α = 0.01

b.t = 2.20, df = 25, α = 0.05

c.t = 5.52, df = 10, α = 0.01

d.t = 2.02, df = 20, α = 0.05

13.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 a health-related hardiness score, measured on a 20-item scale.

c.The IV is maternal breast feeding status (breastfeeds daily vs doesn’t breastfeed); the DV is a maternal bonding with infant score, measured on a 20-item scale.

d.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.

14.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 the PSS score, do a one-way ANOVA to evaluate smoking and PSS scores:

Nonsmokers   Smokers   Quitters

19 31 30

28 29 22

17 22 29

20 29 29

25 28 34

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?  What hypothesis did you test? Did you accept or reject your hypothesis and why?  Copy and Paste your work from StatCrunch into your Word document submission.

15.Looking again at the Fellows Research Group data used in exercise 6 above, perform a one-way ANOVA to examine the mental health scores of the married and divorced and never married subjects. Is the result significant?  What hypothesis did you test? Did you accept or reject your hypothesis and why?  Copy and paste your StatCrunch output into your submission document for full credit.