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Midterm
91. 4. 16
1. (30%)
In a sample of 200 students, 180 used computer frequently.
(a) Develop a 99% confidence interval estimate for the proportion of all
students who used computer frequently.
(b) Develop a 90% confidence interval estimate for the proportion of all
students who used computer frequently.
(c) With a margin of error of 0.08 or less at 95% confidence, what size
sample would be required to estimate the proportion of all students who
used computer frequently?
2. (30%)
Sample assembly times for a particular manufactured part were
8
10
10
12
15
17
Assume that the population has a normal distribution.
(a) Provide a 90% confidence interval for the population mean.
(b) Provide a 99% confidence interval for the population mean.
(c) With a margin of error of 1 or less at 95% confidence, what size
sample would be required to estimate the population mean?
3. (20%)
There are 500 employees in a firm; 45% are union members. A sample of
60 employees is selected randomly.
(a) What is the sampling distribution of
p?
(b) What is the probability that the sample proportion (proportion of
union members) is between 0.40 and 0.55?
4.(15%)
The average weekly earnings of bus drivers in a city are $950 with a
standard deviation of $45. Assume that we select a random sample of 81
bus drivers.
(a) What is the probability that the sample mean will be greater than
$960?
1
(b) If the population of bus drivers consisted of 400 drivers, what would
be the standard error of the mean?
5. (25%)
(a) Let X be binomial random variable with
 3 i
3 i
n  3 (i.e., f (i )  
i
 p 1  p  , i  0, 1, 2, 3.) .
 
For the following hypothesis test
H0 : p 
we reject
H0
as
1
2
vs H a : p  ,
2
3
X  0 or 3 . Please calculate
  the probabilit y of making a type I error
  the probabilit y of making a type II error .
(b) Suppose we have a normal population of 25 elements
6.9
6.9
7.6
6.0
6.5
6.8
6.2
6.5
5.3
7.2
7.8
5.8
7.0
8.6
5.5
7.6
7.6
7.1
6.7
6.0
7.3
7.2
6.6
7.7
7.1
Suppose the first row of the table of random number is
88547 09896 95436 79115 08303 01041 20030 63754 08459 28364
Please use systematic sampling to obtain a sample of 5 elements and
then construct a 95% confidence interval.
2