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Medicine and Clinical Studies
Some physicians use the cholesterol ratio (CR = total cholesterol/HDL cholesterol) as a measure of a patient's risk of heart disease. In addition, the triglyceride concentration (TG) is associated with coronary artery disease in many patients. In a study of the relationship between these two variables, a random sample of adults was obtained, and the triglyceride level (x1, mg/dL) and cholesterol ratio (y) was obtained for each person.
a. Carefully sketch a scatter plot of these data (y versus x1). The relationship does not appear to be linear. Can you describe this relationship between y and x1?
b. Compute the natural logarithm of each difference (x1 2 129). That is, find the values of a new predictor variable, x2 = ln(x1 - 129).
c. Carefully sketch a scatter plot of y versus the new predictor variable x2. Describe this relationship.
d. Find the estimated regression line, and complete the ANOVA table using x2 as the predictor variable.
Give a 95% confidence interval for the difference in bleeding times. Do you think pressure increases mean bleeding time? Why?
A restaurant claims that its speed of service time is less than 18 minutes. A random selection of 36 service times was collected, and their mean was calculated to be 17.7 minutes.
In one-way ANOVA, we were able to determine the confidence interval for the population value of each treatment mean. Why is this not appropriate for the treatments being examined in the randomized block design?
Below is a partial multiple regression computer output based on a quadratic regression model to predict student enrollment at a local university.
The phugoid mode has a natural frequency of 0.1 rad/s, and the short period mode is 1.4 rad/s. The block diagram is shown in Figure CP10.4. (a) Let the lead compensator be
a random variable x has mean mu and standard deviation sigma. suppose n independent observations of x are taken and the
It has been reported that the average US office worker receives 14 fax messages per day. For purposes of this exercise, we will assume that the daily number of fax messages is normally distributed with a standard deviation of 5.0 messages.
Will the between-treatments estimate of variability be larger or smaller than the between-treatments estimate of variability of four means drawn from a population with μ = 100?
Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error?
The random variable X is uniformly distributed on (-1, 2) . Derive the pdf of Y = X2.
Roll a balanced 8-sided die and a balanced 6-sided die and add the spots on the up-faces. Call the sum X. What is the probability distribution of the random variable X?
In each hospital, fifteen patients were treated, each having one of three types of cancer (i.e., there were five patients with each type of cancer). The health of each patient was rated on a ten-point scale after one week, two weeks, and three wee..
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