代写 MA2720

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  • 代写 MA2720

    MA2720
    Homework 5
    Due Tuesday, March 29, 2016
    Name_______________________________
    Class_______________________________
    1. The EPA standard on the amount of suspended solids that can be discharged into rivers and streams is a
    maximum of 60 milligrams per liter daily, with a maximum monthly average of 30 milligrams per liter.
    Suppose you want to test a randomly selected sample of n water specimens and to estimate the mean daily
    rate of pollution produced by a mining operation. If you want a 98% confidence interval estimate of width
    2.2 milligrams, how many water specimens would you have to include in your sample? Assume prior
    knowledge indicates that pollution readings in water samples taken during a day are approximately
    normally distributed with a standard deviation equal to 5 milligrams.
    _________________________________(4)
    If you can only take 75 water samples and you still need to be 98% confident, what is your new confidence
    interval width?
    _________________________________(3)
    If you can only take 75 samples and you still need to be within plus or minus 1.1 milligrams, what is your
    new confidence level?
    _________________________________(4)
    2. One way corporations raise money for expansions to issue bonds, which are loan agreements to repay the
    purchaser a specified amount of money with a fixed rate of interest paid periodically over the life of the bond.
    The sale of the bonds is usually handled by an underwriting firm. Does it pay to shop for your bond
    underwriter? The reason for the question is that the price of a bond may rise or fall after its issuance.
    Therefore, whether a corporation receives the market price for a bond depends on the skill of the underwriter.
    Random and independent samples were taken and the mean change in the price ($) of 27 bonds handled over
    a 12 month period by one underwriter and in the prices of 23 bonds handled by another are given below.
    Underwriter 1 Underwriter 2
    Sample Size 27  23
    Sample Mean -.0491 -.0307
    Sample Variance  0.009800  0.006465
    Assuming normality, construct a 99% confidence interval to determine if there is a difference in mean
    change in bond prices handled by the two underwriters.  (14 points)
    Random Variable_____________________
    Assumptions:____________________________
    _______________________________________
    _______________________________________
    H o _________________________________
    H a _________________________________
    Reliability Coefficient__________________
    (__________________________________)
    Conclusion__________________________
    ____________________________________
    ____________________________________
    ____________________________________
    ____________________________________
    Based on your conclusion, what type of error have you subjected yourself to and explain the error in terms
    of this particular situation? 
    ____________________________________
    ____________________________________
    _________________________________(4)
    3. A pupillometer is a device used to observe changes in an individual’s pupil dilations as he or she is exposed
    to different visual stimuli. There is a direct correlation between the amount an individual’s pupil dilates
    and his or her interest in the stimuli so marketing organizations sometimes use pupillometers to help them
    evaluate potential consumer interest in new products. Suppose 15 consumers were chosen at random and
    each was shown two different silverware patterns. The pupillometer readings (mm) for each consumer
    are shown in the table below. Assuming normality, test at the 10% significance level to determine if the
    mean dilation for pattern 1 exceeds that for pattern 2.  (16 points)
    Consumer  1  2  3  4  5  6  7  8  9  10  11 
    Pattern 1  1.00  0.97  1.45  1.21  0.77  1.32  1.81  0.91  0.98  1.46  1.85
    Pattern 2  0.80  0.66  1.22  1.00  0.81  1.11  1.30  0.32  0.91  1.10  1.60
    Consumer  12  13  14  15 
    Pattern 1  0.33  1.77  0.85  0.15
    Pattern 2  0.21  1.50  0.65  0.05
    Random Variable_____________________
    Assumptions:____________________________
    _______________________________________
    _______________________________________
    H o _________________________________
    H a _________________________________
    Test Statistic_________________________
    Rejection Region______________________
    Conclusion__________________________
    ____________________________________
    ____________________________________
    P-value_____________________________
    4. There are many physical and social pressures that lead many urban bus drivers to retire prematurely with
    disabilities such as coronary heart disease and stomach disorders. An intervention program was
    implemented to improve the work conditions of Stockholm Sweden’s city’s bus drivers and was then
    evaluated. A random and independent samples of bus drivers in the intervention program and bus drivers
    not in the program were taken and the heart rates (in beats per minute) were determined. Assuming
    normality and testing at the 5% significance level, do the data provide sufficient evidence to conclude that
    the intervention program reduces mean heart rate of urban bus drivers in Stockholm? (16 points)

    代写 MA2720

     
    Intervention
    68  66  64  58  69  63  68  63  64  71  67  69  60  61
    No Intervention
    74  62  67  63  77  57  80  77  73  76  54  73  54  60
    77  63  76  74  73  54  60  77  83  60  68  64  66  71 
    Random Variable_____________________
    Assumptions:____________________________
    _______________________________________
    _______________________________________
    H o _________________________________
    H a _________________________________
    Test Statistic_________________________
    Rejection Region______________________
    Conclusion__________________________
    ____________________________________
    ____________________________________
    P-value_____________________________
    If you had tested at the 10% significance level, would your conclusion have changed? Explain.
    ____________________________________
    _________________________________(4)
    5. A study examined the reproductive characteristics of the eastern cottonmouth. Random and independent
    samples were taken of the number of young per litter for female cottonmouths in Florida and in Virginia.
    Preliminary data analyses indicate that you can reasonable presume that litter sizes of cottonmouths in
    both states are approximately normally distributed. At the 1% significance level, do the data provide
    sufficient evidence to conclude that, on average, the number of young per litter of cottonmouths in Florida
    is less than that in Virginia. (10 points)
    Group N  Mean Std. Dev  Std. Error
    Florida 24  5.458 1.587 0.324
    Virginia  26  7.923 2.883 0.565
    If Variances Are  t  Df  Pvalue
    Equal -3.70 48  0.000277 
    Not Equal  -3.78 39.5  0.000259
    H o _________________________________
    H a _________________________________
    Assumptions:____________________________
    _______________________________________
    _______________________________________
    Test Statistic:________________________
    P-Value:____________________________
    Conclusion__________________________
    ____________________________________
    ____________________________________
    ____________________________________

    代写 MA2720