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DEPARTEMEN PENDIDIKAN NASIONAL
UNIVERSITAS ANDALAS
FAKULTAS TEKNIK
JURUSAN TEKNIK INDUSTRI
LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI
TUGAS PENDAHULUAN
ESTIMASI
1.
Many cardiac patients wear implanted pacemakers to control their heartbeat.
A plastic connector module mounts on the top of the pacemaker. Assuming
a standard deviation of 0.0015 and an approximate normal distribution, find
a 95% confidence interval for the mean of all connector modules made by a
certain manufacturing company. A random sample of 75 modules has an
average of 0.310 inch.
2.
A random sample of 12 shearing pins is taken in a study of the Rockwell
hardness of the head on the pin. Measurements on the Rockwell hardness
were made for each of the 12, yielding an average value of 48.50 with a
sample standard deviation of 1.5. Assuming the measurements to be
normally distributed, construct a 90% confidence interval for the mean
Rockwell hardness.
3.
Students may choose between a 3-semcstcr-hour course in physics without,
labs and a 4-semester-liour course with labs. The final written examination
is the same for each section. If 12 students in the section with labs made an
average examination grade of 84 with a standard deviation of 4, and 18
students in the section without labs made an average: grade of 77 with a
standard deviation of 6, find a 99%. confidence interval for the difference
between the average grades for the two courses. Assume the populations to
be approximately normally distributed with equal variances.
4.
In a random sample of 1000 homes in a certain city, it is found that 228 are
heated by oil. Find the 99%, confidence interval for the: proportion of
homes in this city that are heated by oil.
5.
A conjecture by a faculty member in the microbiology department at
Washington University School of Dental Medicine in St. Louis states that a
couple of cups of either green or oolong tea each day will provide sufficient
fluoride to protect your teeth from decay. How large a sample is needed to
estimate the percentage of citizens in a certain town who favor having their
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DEPARTEMEN PENDIDIKAN NASIONAL
UNIVERSITAS ANDALAS
FAKULTAS TEKNIK
JURUSAN TEKNIK INDUSTRI
LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI
water fluoridated if one wishes to be at least 99% confident that the estimate
is within 1% of the true percentage?
6.
A manufacturer of car batteries claims that his batteries will last, on
average, 3 years with a variance of 1 year. If 5 of these batteries have
lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence
interval for a2 and decide if the manufacturer's claim that a" = 1 is valid.
Assume the population of battery lives to be approximately normally
distributed.
7.
The government awarded grants to the agricultural departments of 9
universities to test the yield capabilities of two new varieties of wheat. Each
variety was planted on plots of equal area at each university and the yields,
in kilograms per plot, recorded as fol- lows:
Find a 95% confidence interval for the mean difference between the yields
of the two varieties, assuming the differences of yields to be
approximately normally distributed. Explain why pairing is necessary in
this problem.
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