Tutorial 2 (1) (Estimation)
Given sampling error (margin of error), e  Z / 2
σ
.
n
1. A survey of 30 adults found that the mean age of a person’s primary vehicle is 5.6 years.
Assuming the standard deviation of the population is 0.8 year; find the 90% confidence
interval of the population mean. ~ (5.36, 5.84) years.
2. The college president asks the statistics teacher to estimate the average age of the students at
their college. The statistics teacher would like to be 99% confident that the estimate should be
accurate within 1 year. From a previous study, the standard deviation of the ages is known to
be 3 years. How large a sample is necessary? ~ (60) students
3. A random sample of 6 items taken from a normal population with mean μ and variance 4.5
cm2 gave the following data:
Samples data: 12.9 cm, 13.2 cm, 14.6 cm, 12.6 cm, 11.3 cm, 10.1 cm.
a. Find the 95% confidence interval for μ ~ (10.75, 14.15) cm
b. What is the width of this confidence interval? ~ (3.4) cm
4. In a random sample of 100 batteries produced by a certain method, the average lifetime was
150 hours and the standard deviation was 25 hours
a. Find a 95% confidence interval for the mean life time of batteries produced by this method.
~ (145.1, 154.9) hours
b. Find a 99% confidence interval for the mean life time of batteries produced by this method
~ (143.56, 156.44) hours
c. An engineer claims that the mean life time is between 147 and 153 hours. With what level
of confidence can this statement be made? ~ (77%)
d. Approximately how many batteries must be sampled so that a 95% confidence interval will
specify the mean to within  2 hours? ~ (601) batteries
e. Approximately how many batteries must be sampled so that a 99% confidence interval will
specify the mean to within ±2 hours? ~ (1037) batteries
5. A chemist made 8 independent measurements of the melting point of tungsten. She obtained a
sample mean of 3410.14oC and a sample standard deviation of 1.018oC.
a. Find a 95% confidence interval for the melting point of tungsten ~ (3409.29, 3410.99) oC
b. Find a 99% confidence interval for the melting point of tungsten ~ (3408.88, 3411.40) oC
c. If the eight measurements had been 3409.76, 3409.80, 3412.66, 3409.79, 3409.76,
3409.77, 3409.80, and 3409.78, would the confidence intervals found in parts (a) and (b)
be valid? Explain. ~ (valid: the mean of the sample is between the interval)
The (1-  )100% Confidence Interval for p for Large Samples (n  30)
pˆ  z
2
e  z
pˆ 1  pˆ 
n
pˆ 1  pˆ 
2
n
6. The president of a university would like to estimate the proportion of the student
population that owns a personal computer. In a sample of 500 students, 417 own a personal
computer.
a. Referring to Table 8-10, the critical value for a 99% confidence interval for this sample
is _______. ~ (2.5758)
b. Referring to Table 8-10, a 99% confidence interval for the proportion of student
population who own a personal computer is from _____ to ______. ~ (0.7911, 0.8769)
c. Referring to Table 8-10, the sampling error of a 99% confidence interval for the
proportion of student population who own a personal computer is _______. ~ (0.04286)
7. A recent study of 180 females showed that 25% took vitamins. A medical researcher
whishes to determine the percentage of females who take vitamins. He wishes to be 99%
confident that the estimate is within 2 percentage points of the true proportion. How large
should the sample size be? ~ (3111) females
8. A confidence interval was used to estimate the proportion of statistics students that are
female. A random sample of 72 statistics students generated the following 90% confidence
interval: (0.438, 0.642). Using the information above, what total size sample would be
necessary if we wanted to estimate the true proportion to within 0.08 using 95%
confidence? ~ (150)
9. On a certain day, a large number of fuses were manufactured, each rated at 15A. A sample
of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout
amperages greater than 15A.
a. Find a 95% confidence interval for the proportion of fuses manufactured that day
whose burnout amperage is greater than 15A. ~ (0.1319, 0.3215)
b. Find a 98% confidence interval for the proportion of fuses manufactured that day
whose burnout amperage is greater than 15A. ~ (0.1143, 0.3391)
c. Find the sample size needed for a 95% confidence interval to specify the proportion to
within ±0.05. ~ (270) fuses
d. Find the sample size needed for a 98% confidence interval to specify the proportion to
within ±0.05 ~ (380) fuses
10. A random sample of 400 electronic components manufactured by a certain process are
tested, and 30 are found to be defective.
a. Let p represent the proportion of components manufactured by this process that are
defective. Find a 95% confidence interval for p. ~(0.0492, 0.1008)
b. How many components must be sampled so that the 95% confidence interval will
specify the proportion defective to within ±0.02? ~(667) components
11. A study was conducted to compare the mean number of police emergency calls in two
districts for duration of 24 hours. Samples of number of calls for 100 days were randomly
selected from the police records for each of the two districts. The sample statistics are as
follows:
Sample size
Sample mean
sample variance
Muar
100
2.4
1.44
District
Batu Pahat
100
3.1
2.64
Find a 90% confidence interval for the difference in the mean number of police
emergency call in 24 hours between two districts.
12. An experiment was conducted to compare two diets A and B designed for weight
reduction. The group for diet A comprised of 35 overweight dieters while 30 overweight
dieters for diet B were randomly selected. Their weight losses were recorded after a one
month period. The results are as follows:
Diet A
Diet B
X A  21.3
s A  2.6
X B  13.4
sB  1.9
Construct a 95% confidence interval for the difference in the mean weight loss for the
two diets.
13. 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 the highways. Of the 250 car drivers
interviewed, 220 car drivers were in favour of raising the speed limit while of the 200
motirists interviewed, 180 motorists were in favour. Find a 95% confidence interval for
the difference in proportion between the car drivers and motorist who are in favour of
raising the speed limit.