# 代写 MA2720

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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