Week 2 & 3 assignment – basic biostatistics

14 + 8 Answers and calculations as basic statistics student would explain put into both an MS Excel spreadsheet and copied into MS Word doc format. Due by 7pm 2/2/14. 

 

Week 2 Assignment

  1. A. What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)?   

B. 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)?

 

  1. 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 a t distribution table, 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

66

 

010

68

 

011

78

 

012

89

 

013

91

 

014

81

 

015

77

 

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 one or two sentences that could be used to report the results obtained for the t-test in Exercise 4.

 

 

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 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.

 

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 = 0.01

b.                   t = 2.00, dr = 25, α = 0.05

c.                    t = 5.52, df = 10, α = 0.01

d.                   t = 2.02, df = 150,  α = 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:

X-1

B-1

Z-1

45

55

54

62

55

52

50

54

41

65

44

35

62

52

38

50

69

41

50

58

51

58

45

44

      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  α = 0.01

                b.             F = 5.02, df = 3, 60, α = 0.001

                c.             F = 3.45, df = 3, 27, α = 0.05

                d.             F = 4.99, df = 2, 150, α = 0.01

 

                e.             F = 2.09, df = 2, 250, α = 0.05

 

 ————————————————————————————————————————————-

Week 3 Assignment

 

 

1.         Using StatCrunch, calculate the chi-square statistic and degrees of freedom for the following set of data for 300 people:

 

                                                            Group A          Group B          Group C          Total

                        Had flu shot                     20                   30                    32                   82

                        Didn’t have flu shot         80                   70                    68                 218

                        Total                               100                 100                  100                 300

 

            Is the value of the chi-square statistically significant at the 0.05 level? 

 

2.         Write a paragraph summarizing the results of the analysis in Exercise 1.

 

3.         Using StatCrunch, calculate the chi-square statistic and degrees of freedom for the following set of data for 180 people undergoing a knee replacement treatment with a drug supplement:

 

                                                Treatment with drug X    Treatment without Drug X     Total

            Had > 8 wk rehab                   18                                32                                  50        

Had < 8 wk rehab                   70                                60                                  130

                                    Total                88                                92                                 180

 

            Is the value of the chi-square statistically significant at the 0.05 level? 

 

4.         Write a paragraph summarizing the results of the analysis in Exercise 3.

 

5.         Given each of the following circumstances, determine whether the calculated values of chi-square are statistically significant:

 

a.                   χ2 = 3.02, df = 1, α = 0.05

b.                  χ2 = 8.09, df = 4, α = 0.05

c.                   χ2 = 10.67, df = 3, α = 0.01

d.                  χ2 = 9.88, df = 2, α = 0.01

 

6.         Match each of the nonparametric tests in Column A with its parametric counterpart in Column B

 

            A. Nonparametric Test                        B.  Parametric Test

                  1.  Mann-Whitney U-test                    a.  Paired t-test

                  2.  Friedman test                                 b.  One-way ANOVA

                  3.  Kruskall-Wallis test                        c.  Independent groups t-test

                  4.  Wilcoxon signed-ranks test            d.  Repeated measures ANOVA

 

7.   Using the information provided, indicate which statistical test you think should be used for each of the following situations:

 

a.       Independent variable: normal birth weight vs. low birth weight infants; dependent variable: 1 minute Apgar scores (1-10 scale).

b.      Independent variable: time of measurement (before, during, and after surgery); dependent variable: heart rate.

c.       Independent variable: time of measurement (before, during, and after intervention); dependent variable: did vs did not exercise regularly.

d.      Independent variable: infertility treatment A vs infertility treatment B vs control condition; dependent variable: did vs did not become pregnant.

 

8.         Below are three sets of expected frequencies for the four cells of 2 X 2 contingency tables.  Identify which statistical procedure would be appropriate for each, using the most conservative approach.

 

            a.         4        4                        b.         35          35                  c.         9         9

 

                        21    21                                    65          65                            91       91

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