Download Probability and Statistics EQT 272

SEM II 2015/2016
EQT 271 ENGINEERING STATISTICS
TUTORIAL 2
CONFIDENCE INTERVAL
1) A study was carried out to estimate the mean life of a large shipment of light bulbs. A
random sample of 50 light bulbs was selected and indicated that the sample mean life
was 350 hours and the standard deviation was 100 hours. Construct a 95% confident
interval estimate of the true mean life for all light bulbs in this shipment.
2) The brightness of a television picture tube can be evaluated by measuring the amount
of current required to achieve a particular brightness level. A random sample of 10
tubes indicated a sample mean is 317.2 microamps and a sample standard deviation is
15.7 microamps. Find (in microamps) a 99% confidence interval estimate for mean
current required to achieve a particular brightness level.
3) 30 male undergraduate students and 35 female undergraduate students are randomly
selected from faculty of mechanical engineering. Result for their test are shown below:
Male
xM  82
sM  8
Female
xF  76
sF  6
Assume that both populations are normally distributed and have equal population
variances. Construct a 95% confident interval for the difference in the two means.
Can you conclude that there is a difference in the mean result for male and female
students?
4) A study was conducted to compare the mean number of police emergency calls in two
districts for duration of 24 hours. Samples of calls were randomly selected from the
police records for each of the two districts. The sample statistics are as follows:
District
Muar
Batu Pahat
Sample size
10
15
Sample mean
2.4
3.1
Sample variance
1.44
2.64
Find a 90% confidence interval for the difference in the mean number of police
emergency call in 24 hours between two districts.
5) Two candidates A and B will compete for the post of President of Pulai Golf Club.
From 100 members of the club, 57 prefer voting for A as the president. Construct a
94% confidence interval for the population of all voters who favor candidate A. What
can they assert with 97% confident about the maximum error of their estimate?
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6) Does the M&M Corporation use the same proportion of red candies in its plain and
peanut varieties? A random sample of 56 plain M&Ms contained 12 red candies, and
another random sample of 32 peanut M&Ms contained 8 red candies. Using 95%
confidence interval, can you conclude that there is a difference in the proportions of
red candies for the plain and peanut varieties? Explain.
7) The diameter of a two years old Sentang tree is normally distributed with a standard
deviation of 16 cm. How many trees should be sampled if it is required to estimate the
mean diameter within  15 cm with 95% confidence interval?
HYPOTHESIS TESTING
8) A teacher claims that students in Class A put in more hours studying compared to
other students. The mean numbers of hours spent studying per week is 25 hours with a
standard deviation of 3 hours per week. A sample of 40 Class A students was selected
at random and the mean number of hours spent studying per week was found to be 26
hours. Can the teacher’s claim be accepted at 5% significance level?
9) An experiment is done to test strength of two types of glasses. A sample of 12 pieces
of glasses has a mean strength of 40 kg and a standard deviation of 2 kg. A sample of
13 pieces of glasses has a mean strength of 38 kg and a standard deviation of 2.5 kg.
Test at 5% significance level that the mean strength of the two types of glasses is the
same. Assume the two population variances are equal.
10) A manufacturer of a detergent claimed that his detergent is 95% effective in removing
tough stains. In a sample of 300 people who had used the detergent, 279 people
claimed that they were satisfied with the result. Determine whether the manufacturer’s
claim is true at 1% significance level.
11) The management of Priority Health Club claims that its members lose an average of
10 pounds or more within the first month after joining the club. A consumer agency
that wanted to check this claim took a random sample of 36 members of this health
club and found that they lost an average of 9.2 pounds within the first month of
membership with a standard deviation of 2.4 pounds. Find the p-value for this test.
What will your conclusion be if   0.01? What if   0.05?
12) At Canon Food Corporation, it took an average of 50 minutes for new workers to
learn a food processing job. Recently the company installed a new food processing
machine. The supervisor at the company wants to find if the mean time taken by new
workers to learn the food processing procedure on this new machine is different from
50 minutes. A sample of 40 workers showed that it took, on average, 47 minutes for
them to learn the food processing procedure on the new machine with a standard
#DR. SAFWATI IBRAHIM
deviation of 7 minutes. Find the p-value for the test that the mean learning time for the
food processing procedure on the new machine is different from 50 minutes. What
will your conclusion be if   0.01?
CONFIDENCE INTERVAL & HYPOTHESIS TESTING
13) Selected random sample of 16 packages of a product whose packages are marked as
weighing 1 kg. From the 16 packages: x  1.1kg and s  0.36 kg.
i)
ii)
iii)
Find a 95% confidence interval for the mean weight  of the 1-kg packages.
Should the company’s claim that the mean weight  is 1 kg be challenged?
Explain.
If you decided to use   0.1 do the conclusion would be the same as in (ii)?
14) Two separate surveys were carried out to investigate whether or not the user of Plus
highway were in favor of raising the speed limit on highways. From the 250 car
drivers interviewed, 220 were in favor of raising the speed limit while from the 200
motorist interviewed, 180 were in favor.
i)
Find a 95% confident interval for the difference in proportion between the car
drivers and motorist who are in favor of raising the speed limit.
ii)
Test hypothesis for the difference between car drivers and motorist who were
in favor of raising the speed limit on highways at 1% significance level.
iii)
If you decided to use   0.1 do the conclusion would be the same as in (ii)?
#DR. SAFWATI IBRAHIM