Heart Rates and Blood Pressure Table B.7 shows the heart rates and systolic blood pressure for eight 55-year-old patients from the Intensive Care Unit data introduced in Data 2.3 on page 66 and available at ICUAdmissions. We are testing to see if the data provide evidence of a positive correlation between these two variables for 55-year-old ICU patients.

(a) Define any relevant parameter(s) and state the null and alternative hypotheses.

(b) What assumption do we make in creating the randomization distribution?

(c) What statistic will we record for each of the simulated samples to create the randomization distribution? What is the value of that statistic for the observed sample?

(d) Where will the randomization distribution be centered?

(e) Explain how we can create randomization samples to be consistent with the null hypothesis.

(f) Find one point on the randomization distribution by carrying out the procedure in part (e). Show the resulting values for the variables, and compute the sample correlation for the randomization sample.

(g) Find a second randomization sample and record its sample correlation.

Data 2.3

The dataset ICUAdmissions24 includes information on 200 patients admitted to the Intensive Care Unit at a hospital. Twenty variables are given for the patients being admitted, including age, gender, race, heart rate, systolic blood pressure, whether or not CPR was administered, and whether or not the patient lived or died.

Table B.7

Heart Rate …………… Systolic BP

86 ……………………….. 110

86 ……………………….. 188

92 ……………………….. 128

100 ……………………….. 122

112 ……………………….. 132

116 ……………………….. 140

136 ……………………….. 190

140 ……………………….. 138

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