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Fall 2011
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 105 points available.
1.
(6) You
want to estimate the percentage of California statistics students who get grades of B or higher. How many
such students must you survey if you want 97% confidence that the sample percentage is within 2 percentage point?
2.
(9) A random
smokers.
sample of 139 men contains 26% smokers. Test the claim at 2%-SL that 22% of men population is
3.
(17:3,5,9)
In tests of a computer component, it is found that the mean time between failures is 520 hours. A
modification is made to increase the time between failures. A random sampling resulted in the following times
between failures:
518 548 561 523 536 499 538 557 528 563
a. Find the sample mean.
b. Find the sample standard deviation.
c. AT 5%-SL, test the claim that the mean time between failures has now been greater than 520 hours.
4.
(20:7,7,6) A NAPA Auto
Parts supplier wants information about how long car owners plan to keep their cars. A
simple random sample of 25 car owners results in mean of 7.01 years and standard deviation of 3.74 years.
a. Construct the 99% confidence interval estimate of the population mean.
b. Construct the 99% confidence interval estimate of the population standard deviation.
c. If several years have passed and you need to conduct a new survey to estimate the mean length of time that car
owners plan to keep their cars, how many randomly selected car owners must you survey? Use 95%
confidence-level and make the sample mean is within 0.25 years of the population mean.
5.
(9)
The standard deviation of math test scores at one high school is 16.1. A teacher claims that the standard deviation
of the girls’ test scores is smaller than 16.1. A random sample of 22 girls results in scores with a standard deviation
of 13.3. Use a significance level of 0.01 to test the teacher’s claim.
6.
(31:3,5,7,7,9) Suppose
that the weight of the cereal in boxes of Loopy Froots breakfast cereal is normally
distributed. A consumer advocate group randomly sampled 8 boxes of Loopy Froots and weighed the
contents (in grams): 535, 540, 565, 575, 535, 558, 564, and 550.
a. Find the mean of the sample.
d. Construct 95%-CI for standard deviation.
b. Find the standard deviation of the sample.
e. At 5%-SL, test the claim that the weight of
c. Construct 90%-CI for mean.
the cereal in boxes of Loopy Froots
breakfast is less than 570 grams.
7.
Two methods of chemical reduction are being studied in 7 different locations. Both methods are
applied to all locations and the total chemical reduction was recorded:
(14)
Method 1: 1.3 3.0 1.5 5.5 0.7 0.2 1.0
Method 2: 1.4 5.8 1.7 3.9 1.7 0.1 1.3
At 5%-SL, do these data indicate any difference in the reduction of chemical between two methods?