Week2Assignment 322

1. What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)? 3/36 or 8.33%. What is the probability that a player can roll a four 3 times in a row (assume that rolling the dice each time does not affect the outcome of the next roll)? 3/36 x 3/36 x 3/36 = 27/46656 = 3/5184

2. Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why? Despite, both Population A and Population having a mean height of 70.0 inches with an SD of 6.0, Population B will probably yield a more accurate estimate of its population mean. The reason for this is because Population B’s random sample of 50 people is greater than Population A’s random sample of 30 people. The additional 20 people difference in Population B allows the average amount of error of its sample means (SEM) to be smaller. The smaller the SEM, the more accurate are the sample means as estimates of the population value.

3. Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 50 patients. The mean vein size is found to be 7.8mm with an SD of 2.1. Using a t distribution table, what are the confidence limits for a 95% confidence interval? For a 99% confidence interval?
95% confidence interval results: μ : population mean

Confidence limits for a 95% confidence interval are 7.2031865 ≤ 7.8 ≤ 8.396813

99% confidence interval results: μ : population mean

Confidence limits for a 99% confidence interval are 7.004095 ≤ 7.8 ≤ 8.595905

4. In a pilot study evaluating the use of a new drug to lower resting heart rates (HR) of patients, the following data was recorded:
Subject #
Resting HR
001
72

002
88

003
71

004
87

005
64

006
77

007
79

008
59

009
66

010
68

011
78

012
89