# Project #16807 - Biostats

[Gotta show work! :( ]

1- (3 points) The following table represents a summary of a study on a relationship

between smoking (smokers, nonsmokers) and alcohol consumption (none, low, medium,

high). Test the hypothesis of independence between the two variables at = 0:05. You

Alcohol

None Low Medium High Total

Smokers 1880 2048 194 76 4198

Nonsmokers 4290 2430 172 37 6929

Total 6170 4478 366 113 11127

2- (2 points) in a study-induced anaphylaxis among patients taking rocuronium bromide

as part of their anesthesia, Laake and Rottingen found that the occurrence of anaphylaxis

followed a Poisson model with  = 12 incidents per year in Norway. find the

probability that in the next year, among patients receiving rocuronium, exactly three

will experience anaphylaxis.

3- (3 points) A study is conducted in which a gold standard invasive ( i.e., blood drawn)

method of monitoring glucose in diabetic patients is compared to a newly developed

non-invasive ( i.e., no blood drawn) monitoring method in order to determine whether

the two systems produce equivalent results. To this end, each of the monitoring devices

is simultaneously employed to assess glucose levels in ten diabetic patients. The two

measures for each patient are provided below.

Test the hypothesis of no difference between the two test.

Invasive Non-invasive

140 144

84 82

200 200

249 247

71 64

131 138

140 132

122 123

139 146

119 117

4- (4 points) Given the following data

X Y

131 138

140 132

122 123

139 146

119 117

140 144

84 82

200 200

249 247

71 64

(a) Find the correlation coefficient between X and Y .

(b) Is there any evidence of a linear relationship between X and Y ? Justify

(c) A linear model fit predicting Y as a function of X produces the following output

Estimate Std. Error t value P-value

(Intercept) -2.10051 5.15257 -0.408 0.694

x 1.01362 0.03483 29.101 2.11e-09

Using the output, write down the regression model. What is the predicted value of Y

when X = 105?

5- (2 points) The following 2 by 2 table gives the summary of a study on the relationships

between smoking and Heart Disease. Find the risk ratio and interpret your findings

Risk factor Heart Disease Present Heart Disease Absent Total

Smoker 25 10 35

Nonsmoker 14 51 65

6- (2 points) Police report that 78% of drivers stopped on suspicion of drunk driving are

given a breath test, 36% a blood test, and 22% both test. What is the probability that

a randomly selected DUI suspect is given

(a) a test?

(b) neither test?

7- (2 points) What statistical test will you use for testing

(a) the difference in means between two groups

(b) the difference in means in more than two groups

(c) the difference in proportion between two groups

(d) the strength of association between two categorical variables such as smoking (yes,

no) and drinking (none, low, medium, high)

(e) the strength of linear association between two continuous variables

8- (2 points) The Army General Classification Test, or AGCT, is an aptitude test whose

score X is normally distributed with mean 100 and standard deviation 20. Find the

following:

(a) The probability that an AGCT score is between 76 and 120.

(b) The probability that the mean score x of a sample of n = 64 soldiers is greater than

97.

9- (2.5 points) Let i be the average yield in bushels per acre of variety i of corn,

i = 1; 2; 3; 4. In order to test the hypothesis H0 : 1 = 2 = 3 = 4 at the 5% significance

level, four test plots for each of the four varieties of corn are planted. Determine

whether we accept or reject H0 if the yield in bushels per acre of the four varieties of

corn are, respectively, as follows:

X1: 68.82 76.99 74.30 78.73

X2: 86.84 75.69 77.87 76.18

X3: 90.16 78.84 80.65 83.58

X4: 61.58 73.51 74.57 70.75

10- (2.5 points) Each of three cars is driven with each of four different brands of gasoline.

The number of miles per gallon driven for each od the ab = (3)(4) = 12 different

combinations is recorded below.

Gasoline

Car 1 2 3 4

1 26 28 31 31

2 24 25 28 27

3 25 25 28 26

Test the hypothesis that we can expect the same mileage for each of these three type of

cars at = 0:01.

 Subject Mathematics Due By (Pacific Time) 11/15/2013 12:00 am
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