# 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

 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.

 Subject Mathematics Due By (Pacific Time) 11/05/2013 05:00 pm
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