# MATHEMATICS

BST 322 Week 2 Assignment

1. 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 2nd part of Q1 use the multiplicative/consecutive rule

1. 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

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