Test 5 1) You a completing an exam with only multiple-choice questions. There are 20 questions, each of which has 4 options (a, b, c, and d). Suppose you did not study for the exam and must guess at...

Test 5
1) You a completing an exam with only multiple-choice questions.  There are 20 questions, each of which has 4 options (a, b, c, and d).  Suppose you did not study for the exam and must guess at every question.  Let x be the number of co
ect guesses.  In the following questions you will verify that x follows a binomial probability distribution and determine n, p, and q.
Question 1 - Are there a fixed number of trials?
Question 2 - What is n?
Question 3 - Does each trial have only two categories?
Question 4 - How many categories are there for each question?
Question 5 - What is the probability of getting a co
ect answer?
Question 6 - What is the probability of getting an inco
ect answer?
2) You are taking a 20 question True False exam, answer the following 4 questions (enter your answer in decimal format to three significant digits 15% is .150):
Question 1 - What is your probability of getting 15 questions co
ect? p(x=15| n=20, p = .5)
Question 2 - What is your probability of getting more 15  or more questions co
ect? P(x≥15|n=20, p= .5)
Question 3 - What is the probability of getting 15 or less questions co
ect? P(x≤15| n=20,
p=.5)
Question 4 - What is the probability of getting 3 or less questions co
ect? P(x ≤3| n=20, p=.5)
3) A can of ma
les has 40% red ma
les.  You select 20 ma
les blindfolded.  Answer the following questions:
Question 1 - What is the mean number of red ma
les that should be in your sample?
Question 2 - What is the standard deviation of red ma
les that should be in your sample?
Question 3 - You get 7 red ma
les out of 20, is that unusual (calculate the z-score and decide if it is greater than 2 or less than -2 to be considered unusual)?
Question 4 - You get 11 red ma
le out of 20 is that unusual?
4) Use The Cumulative Standard Normal Distribution (z-table) to find the following probabilities (to four decimal places .1234 or .1240):
Question 1 - P(Z≤≤ {"version":"1.1","math":"mo>≤
mo
math>"}1.25)
Question 2 - P(Z > 1.25)
Question 3 - P(Z≤≤ {"version":"1.1","math":"mo>≤
mo
math>"}-1.25)
Question 4 - P(Z > -1.25
5) The mean heart rate of all women is greater than 80 beats per minute.  State the Claim, the null hypothesis, and the alternate hypothesis
6) Most People prefer Chocolate ice cream.  State the claim, null, and alternate hypothesis
7)
    For each of the following (a, b, and c) state the claim, null and alternate hypothesis, define what μ or p re
presents, and whethe
    
    
    
    
    the test is right-tailed, left-tailed, or two-tailed. Use math notation (> < = ≠)
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    For all of the problems in this week's homework
    
    a.
    The folks at the Better Business Bureau claim that the mean volume of all 12 ounce
    you may copy and paste the following math
    
    
    cans of Fizzy Pop is less than the published 12 ounces
    
    
    
    symbols
    
    
    
     
    
    
    
    
    
    
    
    
    
    
    ≥
    
    
    
    
     
    
    
    Variable
    Value
    
    
    
    
    
    
    ≤
    
    
    
     
    
    
    Claim
     
    
    
    
    
    
    
    ≠
    
    
    
     
    
    
    H0
     
    
    
    
    
    
    
    
    H0
    d.f.
    
     
    
    
    H1
     
    
    
    
    
    
    
    
    H1
    
    
     
    
    
    μ
     
    
    
    
    
    
    
    σ
    Zα/2
    
    
     
    
    
    P
     
    
    Test type = Righ
t Tailed, Left Ta
iled, or Two tail
ed
    μ
    tα
    
     
     
    
    
    Test Type
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    b.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    BP claims the mean daily flow rate4 of oil from the damaged Deep Horizon well was about 25,000
ba
els per day
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Value
    
    
    
    
    
    
    
    
    
    
    
    
    
    Claim
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    H0
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    H1
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    μ
     
    
    Test type = Righ
t Tailed, Left Ta
iled, or Two tail
ed
    
    
    
    
    
    
    
    P
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    Test Type
     
    
    
    
    
    
    
    
    
    
    
    
    
    c.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    The American Mathematical Associatioin claims that more than 40% of all people dislike statistic
s
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Value
    
    
    
    
    
    
    
    
    
    
    
    
    
    Claim
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    H0
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    H1
     
    
    Test type = Righ
t Tailed, Left Ta
iled, or Two tail
ed
    
    
    
    
    
    
    
    μ
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    P
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    Test Type
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
8)
    In Sludge county, a sample of 50 randomly selected citizens were tested for pinworm. Of these 10 tested
positive (20%)
     
    The CDC reports that the U.S. average infection rate is 12%. Conduct the following hypothesis tests and
finish with
    
    co
ect disposition of the null hypothesis and conclusions regarding the claim
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    For all of the problems in this week's homework
    a.
    Test the claim that Sludge county has a pinworm infection rate that is greater than the national
average
    you may copy and paste the following math
    
    Use a 0.05 significance level
    
    
    
    
    
    
    
    symbols
    
    
    
    
    
    
    
    
    
    
    
    ≥
    
    Step 1.
    Claim
     
    
    
    
    
    
    
    
    ≤
    
    
    H0
     
    
    
    
    
    
    
    
    ≠
    
    
    H1
     
    
    
    
    
    
    
    
    
    
    
    n
     
    
    
    
    
    
    
    
    
    
    
    α
     
    
    
    
    
    
    
    
    σ
    
    
    P
     
    
    
    
    
    
    
    
    μ
    
    
    
     
    
    
    
    
    
    
    
    
    
    
    q
     
    
    
    
    
    
    
    
    
    
    
    Tailed?
     
     (right, left, or two)
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 2.
    Calculate the test statistic
     
     Create an excel formula in cells F19 to calculate the test statistic
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 3.
    Critical value at 0.05=
    
     
     Obtain from the tables
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 4.
    Dispose of the Null Hypothesis as you were shown in the
Textbook
    
    
    
    
    
    
     
    
    
    
    
    Conclusion regarding the Claim as you were shown in the
Textbook.
    
    
    
    
    
    
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    
9)
    
    In a recent study of Binge Drinking among college students, the U.S. Department of Health defines bin
ge drinking as
    
    consuming 5 or more drinks in a row for me and 4 or more for women. In a recent study of 1200 stud
ents, 564 of them
    
    reported to have engaged in binge drining in the past two weeks.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    a.
    The report concluded that half of all students bing drink. Test this claim at the 0.01 signific
ance level
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 1.
    Claim
     
    
    
    
    
    
    
    
    
    
    
    
     H0
     
    
    
    
    
    
    
    
    
    
    
    
     H1
     
    
    
    
    
    
    
    
    
    
    
    
     n
     
    
    
    
    
    
    
    
    
    
    
    
     α
     
    
    
    
    
    
    
    
    
    
    
    
     P
     
    
    
    
    
    
    
    
    
    
    
    
    
     
    
    
    
    
    
    
    
    
    
    
    
     q
     
    
    
    
    
    
    
    
    
    
    
    
     Tailed?
     
     (right, left, or two)
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 2.
    Calculate the test statistic
     
     Create an excel formula in cells F20 to calculate the test statistic
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 3 .
    Critical value at 0.01=
     
     Obtain from the tables
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Step 4.
    Dispose of the Null Hypothesis as you were sho
wn in the textbook