Brigham and Women’s Hospital reports that approximately 20% of American males and 10% of American females will develop a kidney stone at some time in their life.32 Some research suggests that drinking...

Brigham and Women’s Hospital reports that approximately 20% of American males and 10% of American females will develop a kidney stone at some time in their life.32 Some research suggests that drinking lots of sugar-sweetened soda may lead to an increased risk of developing a kidney stone. A sample of patients who were admitted to Brigham and Women’s Hospital for a kidney stone was obtained. Low-dose computed tomography was used to measure the size (in ml) of each stone, and the ordered observations were recorded. Use the runs test with the normal approximation and a = 0.05 to determine whether there is any evidence that the order of kidney stone sizes is not random with respect to the median size, 3.0 ml. Find the p value associated with this test.

The purpose of this exercise is to determine whether a random number generator really produces a random sequence of observations. Using your graphing calculator or favorite statistical software:

a. Generate 100 observations from a standard normal distribution.

 b. Classify each observation as either above or below the mean (and median) 0.

 c. Conduct a runs test using the normal approximation to determine whether there is any evidence to suggest that the sequence of observations is not random with respect to the mean. Use a = 0.05. Do this 100 times. How many times did you reject the null hypothesis H0: The sequence is random? Draw a conclusion about the sequence of observations produced by your random number generator.