statistics 5

STA2303 Fall 2014

Assignment 5

Name:

UTSA ID:

 Use this page as a cover sheet. Show your work for full credit.

Problem 1

In a study conducted at the Virginia Polytechnic Institute and State University, the plasma

ascorbic acid levels of pregnant women were compared for smokers versus nonsmokers.

Thirty-two women in the last three months of pregnancy, free of major health disorders, and

ranging in age from 15 to 32 years, were selected for the study. Prior to the collection of 20 ml

of blood, the participants were told to avoid breakfast, forgo their vitamin supplements, and

avoid foods high in ascorbic acid content. From the blood samples, the following plasma

ascorbic acid values of each subject were determined in milligrams per 100 milliliters:

Plasma Ascorbic Acid Values

Nonsmokers Smokers

0.97 1.16 0.48

0.72 0.86 0.71

1.00 0.85 0.98

0.81 0.58 0.68

0.62 0.57 1.18

1.32 0.64 1.36

1.24 0.98 0.78

0.99 1.09 1.64

0.90 0.92

0.74 0.78

0.88 1.24

0.94 1.18

Assume that the two sets of data came from normal populations.

(a) Compute the sample means and standard deviations for each group.

(b) Produce a histogram for each group. Use intervals of size 0.2, starting with 0.4. Do you

think the assumption of normality is reasonable for each group? Explain.

(c) Create a 95% confidence interval for the difference in mean plasma ascorbic acid levels

between smokers and interpret.

(d) Is there sufficient evidence at the 5% significance level to conclude that the mean

plasma ascorbic acid levels of smokers is higher than that of nonsmokers?

(e) Summarize your conclusions about this study. Support with any of the above results.

Discuss concerns about the study and anything that might affect your interpretation of

the results.

Problem 2

Fit a regression line to the following data representing age in years (xi) and systolic blood

pressure of healthy adults (yi).

(a) Produce a scatter plot to illustrate the data.

(b) Calculate the sample average age and systolic blood pressure.

(c) Fill in the following table:

)(agex i

)(SBPy i

)( xx i  )( yy

i  2)( xx

i  ))(( yyxx

ii 

20 120

43 128

63 141

26 126

53 134

31 128

58 136

46 132

70 144

19 121

***** TOTAL

(d) Write the prediction equation using proper notation.

(e) What is the predicted increase in systolic blood pressure for each year a person ages?

(f) What is the predicted systolic blood pressure for a healthy newborn?

(g) What is the predicted SBP for a healthy 30 year old?

(h) If one’s SBP is 120, how old does the regression line predict the person to be?

(i) Calculate the coefficient of determination and interpret.

(j) Test the hypothesis that the population slope equals ½ against a two-sided alternative,

at the 5% level of significance, and interpret.

(k) NIH studies have shown that the systolic blood pressure of a newborn is actually around

60. Is there evidence in this sample to suggest that the sbp of a newborn is not 60?

How can you explain the discrepancy?