Assignment 1
The data set lowbwt contains information for a sample of 100 low birth weight infants born in two teaching hospitals in Boston. Systolic blood pressure measurements are saved under the variable name sbp and gender - under the name sex (1-male, 0-female). Values of the Apgar score recorded five minutes after birth – an index of neonatal asphyxia or oxygen deprivation – are saved under the name apgar5. The Apgar score is an ordinal random variable that takes values between 0 and 10. The values of gestational age were saved under the name gestage. Indicators of maternal diagnosis of toxemia during the pregnancy are saved under the variable name tox (1-yes, 0 - no). The variable grmhem is a dichotomous random variable indicating whether an infant experienced a germinal matrix hemorrhage
(1 – a hemorrhage occurred, 0 - not).
1)
(a) Estimate the proportion of low birth weight infants whose mothers experienced toxemia during pregnancy.
(b) Test the null hypothesis that there is no association between occurrences of a germinal matrix hemorrhage for children whose mothers were diagnosed with toxemia relative to children whose mothers were not. What do you conclude?
2)
(a) Construct a histogram of systolic blood pressure measurements for this sample. Based on the graph, do you believe that blood pressure is approximately normally distributed?
(b) Assuming equal variances for males and females, use the two-sample t-test to evaluate the null hypothesis that among low birth weight infants, the mean systolic blood pressure for girls is identical to that for boys.
(c) Even though there are only two populations instead of three or more, test the same null hypothesis using the one-way analysis of variance. Compare the results. What do you conclude?
3)
(a) Construct a pair of box plots of five-minute Apgar score for males and females.
(b) Test the null hypothesis that among low birth weight infants, the median Apgar score for boys is equal to the median score for girls. What do you conclude?
4)
(a) Estimate the correlation of the random variables systolic blood pressure and five-minute
Apgar score for this population of low birth weight infants.
(b) Does Apgar score tend to increase or decrease as systolic blood pressure increases?
(c) Test the null hypothesis
Ho: ρ = 0.
What do you conclude?
5)
(a) Construct a two-way scatter plot of systolic blood pressure versus gestational age. Does the graph suggest anything about the nature of the relationship between these variables?
(b) Using systolic blood pressure as the response and gestational age as the explanatory variable, compute the least-squares regression line. Interpret the estimated slope and yintercept of the line; what do they mean in words?

(c) Suppose that you randomly select a new child from the population of low birth weight infants with gestational age 31 weeks. What is the predicted systolic blood pressure for this child?