Download T3 - HarjunoXie.com

Fall 2010
Math 227
Test 3
Name: ______________________
Show your work clearly, neatly, and understandably. Make sure you round the decimal for probability to 5-decimal place and round
the percentage to 3-decimal. There are 110 points available.
1.
(10)
In a poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all incomes on
tax returns. Construct a 95% confidence interval estimate of the proportion of all adults who have that
belief.
2.
(15: 7,4,2,2)
UCNW Mathematics Department wants to estimate the average age of students applying to their
graduate program with 95% confidence. Suppose the standard deviation of the ages is 7 years.
a. If the desired margin of error 3 years. Find the minimum sample size.
b. If the desired margin of error is halved to 1.5 year. Find the minimum sample size.
c. State the relationship between your answer in part (a) and part (b): The minimum sample size in part
(b) is (approximately) _______ times the minimum sample size in part (a).
d. If the desired margin of error is changed to 1 year, then the minimum sample size is (approximately)
_______ times the minimum sample size in part (a).
3.
Find the critical values.
a. Assume that the normal distribution applies. Find the critical values.
(10: 2,4,4)
Right-tailed test;   0.03 .
b. Assume that t-distribution applies. Find the critical values.
Left-tailed test;   0.025 , and n = 23.
c. Assume that the chi-square distribution applies. Find the critical values.
Right-tailed test;   0.01 , n = 23.
4.
(10) A simple
random sample of 32 cars yields a mean weight of 3605.3 lbs, a standard deviation of 501.7
lbs., and the sample weight appears to be from a normal distributed population. Construct a 95%-CI for
the standard deviation.
5.
(15) According
to Crime in the United States, a publication of the FBI, the mean value lost to purse
snatching was $356 in 2008. For last year, 12 randomly selected purse-snatching offenses yielded the
following values lost, to the nearest dollar. At the 2% significance level, test the claim that the mean value
lost to purse snatching has decreased from the 2008 mean. Assume the population has normal distribution.
231 446 296 386 189 293 261 250 229 372 290 454
6.
(15) In
one trip of the Royal Caribbean cruise ship Freedom of the Seas, 338 of the 3823 passengers become ill with
a Norovirus. At about the same time, 276 of the 1652 passengers on the Queen Elizabeth II cruise ship became ill
with a Norovirus. Treat the sample results as a simple random sample from large populations, and use a 0.01
significance level to test the claim that the rate of Norovirus illness on the Freedom of the Seas is less than the rate
on the Queen Elizabeth II.
7.
(15) A company
is about to test the effectiveness of their newly invented gas mileage additive. Ten cars are selected
at random to a test. They are driven both with and without the additive. The resulting gas mileages are provided
below. Test the company’s claim that the additive very-significantly increases the mileage of a car. Here is the data:
Car
#1
Additive 25.7
No Add 24.9
#2
#3
#4
#5
#6
#7
#8
#9
#10
20.00
18.8
28.4
27.7
13.7
13.0
18.8
17.8
12.5
11.3
28.4
27.8
8.1
8.2
23.1
23.1
10.4
9.9
8.
Listed below are ten voltage levels recorded in Melanie’s home on ten different days. These values
come from a normally distributed population. Use the sample data to construct a 95% confidence interval
(10)
estimate of the standard deviation of all voltage level.
123.3 123.5 123.7 123.4 123.6 123.5 123.5 123.4 123.6 123.8
9.
Listed below are ten voltage levels reported by Thomas. BECAUSE OF HIS LAZINESS, he
subtracted each the data in #8 by 123:
0.3 0.5 0.7 0.4 0.6 0.5 0.5 0.4 0.6 0.8
a. Compute the sample mean
(10:2,4,2,2)
b. Compute the standard deviation.
c. Find the difference of the sample mean in #8 and the sample mean in #9.
d. Find the difference of the sample standard deviation in #8 and the sample standard deviation in #9.