MATHEMATICS
BST 322 Week 2 Assignment
- What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)? 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)?
TIPS: Probability is a fraction or decimal = Number of ways it can happen/Total Number of Possibilities
STEP A: Total Number of possibilities = 36 as follows:
(1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) |
(2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) |
(3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) |
(4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) |
(5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) |
(6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) |
STEP B: Determine the number of ways it can happen for a 4 using two dice.
STEP C: Form the Fraction: Number of ways it can happen/Total Possibilities.
For the 2^{nd} part of Q1 use the multiplicative/consecutive rule
- Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 35 people is picked from population A, and random sample of 65 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why?
TIP: See page 90. You can also calculate the SEM and compare the two values.
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 9.7mm with an SD of 2.5. Using a t distribution table, what are the confidence limits for a 95% confidence interval? For a 99% confidence interval?
TIP: Please use either StatCrunch – 1-SAMPLE T-TEST (Summary) on a blank sheet or the formula on page 94.
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 | 65 | |
006 | 77 | |
007 | 79 | |
008 | 59 | |
009 | 75 | |
010 | 68 | |
011 | 78 | |
012 | 90 | |
013 | 91 | |
014 | 81 | |
015 | 85 | |
016 | 75 | |
017 | 69 |
Given that the average resting HR of the general population for this study is 72, use StatCrunch to perform the appropriate t test. What is the value of t? Using an alpha of 0.05, is the t statistic significant? Why? What are the confidence limits for a 95% confidence interval here and what do they mean for this patient group? Copy and Paste your work from StatCrunch into your Word document submission.
TIP: USE STATCRUNCH – 1-SAMPLE. Remember to input 72 as per the screen below
5. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 4.
TIP: For the report, please use the specific t-test value, the p-value from the test, state whether the result is significant or not and whether you would reject/accept the null hypothesis