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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