Project #15600 - Biostats

Chapter 9

Construct a scatterplot, find the value of the linear correlation coefficient r and use a significance level of α= 0.05 to determine whether there is a significant linear correlation between the two variables:

Pg 443, 11.) Fourteen different second-year medical students took blood pressure measurements of the same patient and results are listed below. Is there a correlation between systolic and diastolic blood pressure values? Apart from correlation, is there some other method that might be used to address an important issue suggested by the data?

 

Systolic

125

107

126

110

110

107

113

126

Diastolic

78

54

81

68

66

83

71

72

 

 

 

Pg 461, 5.) Use the given data to find the equation of the regression line.

X

0

1

2

3

4

Y

4

1

0

1

4

 

_______________________________________________________________________________________________________

Pg470, 5.) Refer to information from Minitab listed below that was obtained by using the paird data consisting of neck size (in inches) and weight (in pounds) for the sample of bears. Along with the paired sample data, Minitab was also given a neck size of 25.0in. to be used for predicting the weight. Test slope.

 

Using the information provided in the display determine the value of the linear correlation coefficient. Given that there are 54 pairs of data, is there a significant linear correlation between bear neck sizes and bear weights?

 

Minitab

The regression equation is WEIGHT= -232 + 20.2 NECK

Predictor

Coef

SE Coef

T

P

Constant

-231.70

22.78

-10.17

0.000

NECK

20.169

1.069

18.86

0.000

 

S= 43.9131         R-Sq= 87.2%     R-Sq(adj)= 87.0%

 

Predicted Values for NEW observations

New Obs

Fit

SE Fit

95% CI

95% PI

1

272.53

7.64

257.21, 287.85

183.09, 361.97

 

 

 

 

 

 

Pg 480, 1.) Refer to the SPSS display that follows & answer the question. The SPSS display is based on sample of 54 bears.


Identify the multiple regression equation that expresses weight in terms of head length, length, and chest size.

Test Model

Test Individual variable

 

 

SPSS

Model Summary

Model

R

R square

Adjusted R square

Std Error of the estimate

1

0.963a

0.928

0.924

33.656

a.     Predictors: (Constant), Distance around the chest, Length of Head, Length of body

 

 

 

 

 

ANOVAb

Model

Sum of Squares

Df

Mean Square

F

Sig

1 Regression

729645.5

3

243215.153

214.711

0.000a

   Residual

56637.875

50

1132.758

 

 

  Total

786283.3

53

 

 

 

 

 

 

 

Coefficients

                                                                                         

Model

Unstandardized Coefficients

B                         Std.Error

Standard Coefficients

Beta

t

(t ratio)

Sig

(p)

1. (constant)

-271.711          31.617

 

-8.594

0.000

Length of head

-.870                  5.676

-0.015

-0.153

0.879

Length of body

.554                    1.259

0.049

0.440

0.662

Distance around chest

12.153                1.116

0.933

10.891

0.000

 

 

 

 

 

Chapter 10

 

Pg 500, 11.) Based on genotypes of parents, offspring are expected to have genotypes distributed in such a way that 25% have genotypes denoted by AA, 50% have genotypes denoted by Aa, and 25% have genotypes denoted by aa. When 145 offspring are obtained, it is found that 20 of them have AA genotypes, 90 have Aa genotypes, and 25 have aa genotypes. Test the claim that the observed genotype offspring frequencies fit the expected distribution of 25% for AA, 50% for Aa, and 25% for aa. Use significance level of 0.05.

 

P 515, 7.) The accompanying table summarizes successes and failures when subjects used different methods in trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the CDC. Use a 0.05 significance level to test the claim that success is independent of the method used. If someone wants to stop smoking, does the choice of the method make a difference?

 

 

Nicotine Gum

Nicotine Patch

Smoking

191

263

Not Smoking

59

57

 

Repeat exercise after adding:

 

 

Nicotine Gum

Nicotine Patch

Nicotine Inhaler

Smoking

191

263

95

Not Smoking

59

57

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 11

Pg 546, 3.) A random sample of males who finished the New York Marathon is partitioned into three categories with ages 21-29, 30-29, & 40 or over. The times (in seconds) are obtained from a random sample of those who finished. The analysis of variance results obtained from Excel are shown below.

 

a.)   what is the null hypothesis?

b.)  What is the alternative hypothesis

c.)   Identify the value of the test statistic

d.)  Find the critical value for a 0.05 significance level

e.)   Indentify the P-value

f.)    Is there sufficient evidence to support the claim that men in the different age categories have different mean times?

 

 

Excel

Source of variation

SS

df

MS

F

P-value

F crit

Between groups

3532063.284

2

1766031.642

0.188679406

0.828324293

3.080387501

Within Groups

1010875649

108

9359959.71

 

 

 

Total

1014407712

110

 

 

 

 

 

 

 

Pg 558 8. & 9.) USE THESE TABLES:

 

Times in seconds for New York Marathon Runners

Age

 

                        21-29                         30-39                         40 & over

                        13, 615                       14,677                                    14,528

                        18,784                                    16,090                                    17,034

                        14,256                                    14,086                                    14,935

Male                10,905                                    16,461                                    14,996

                        12,077                                    20,808                                    22,146

 

 

Female            16,401                                    15,357                                    17,260

                        14,216                                    16,771                                    25,399

                        15,402                                    15,036                                    18,647

                        15,326                                    16,297                                    15,077

                        12,047                                    17,636                                    25,898

 

 

Dependent Variable: TIME

Source

Type III Sum of Squares

Df

Mean square

F

Sig

Model

8292665892a

6

1367110967

151.422

0.000

GENDER

15225412.8

1

15225412.80

1.686

0.206

AGE

92086979.4

2

46043489.70

5.100

0.014

GENDER*AGE

21042068.6

2

10521034.30

1.165

0.329

Error

216683456

24

9028477.350

 

 

Total

8419349258

30

 

 

 

 

a. R squared=0.974 (Adjusted R squared= 0.968)

 

 

8.) Interaction Effect. These the null hypothesis that the times are not affected by  an interaction between gender and age category. What do you conclude?

 

9.) Assume that the marathon running times are not affected by an interaction between gender and age category. Is there sufficient evidence to support the claim that gender has an effect on running times?

 

 

           

Pg 558. Refer to the display which is from 24 subject that were given hearing tests using four different lists of words. The 24 subjects had normal hearing and the tests were conducted with no background noise. The main objective was to determine whether the four lists are equally difficult to understand. In the original table of hearing test scores, each cell has one entry.

 

Analysis of Variance for Hearing

Source

DF

SS

MS

F

P

Subject

23

3231.6

140.5

3.87

0.000

List

3

920.5

306.8

8.45

0.000

Error

69

2506.5

36.3

 

 

Total

95

6658.6

 

 

 

 

11.) Assuming that there is no effect on hearing test scores from an interaction between subject and list, is there sufficient evidence to support the claim that the choice of subject has an effect on the hearing test score? Interpret the results by explaining why it makes practical sense.

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