Download An Introduction to Statistics Course (ECOE 1302)

The Islamic University of Gaza
Faculty of Commerce
Department of Economics and Political Sciences
An Introduction to Statistics Course (ECOE 1302)
Spring Semester 2016 - 6/4/2016
Midterm Exam
Name:___________________________________________ ID:___________
Instructors: Dr. Nafez Barakat
Mr. Ibrahim Abed
Question # 1.Choose the one alternative that best answers the question.(10 points).
1. For a 99% confidence interval of the population mean based on a sample of n = 25
with s = 0.05, the critical value of t is:
a) 2.7970
b) 2.7874
c) 2.4922
d) 2.4851
2.The classification of student major(accounting , economics , management ,
marketing , others) is an example of
a)
b)
c)
d)
a categorical random variable.
a discrete random variable.
a continuous random variable.
a parameter.
3.A 99% confidence interval estimate can be interpreted to mean that
a) if all possible samples are taken and confidence interval estimates are
developed, 99% of them would include the true population mean somewhere
within their interval.
b) we have 99% confidence that we have selected a sample whose interval does
include the population mean.
c) Both of the above.
d) None of the above.
4. In aright _ skewed distribution
a) The arithmetic mean equals the median.
b) The arithmetic mean is less than the median.
c) The arithmetic mean is larger than the median.
d) None of the above.
5. According to the chebyshev rule , at least what percentage of the observations in any
data set are contained within a distance of 3 standard deviations around the mean ?
a) 67% .
b) 75% .
c) 88.89%.
d) 99.7% .
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6.When extreme values are present in a set of data, which of the following descriptive
summary measures are most appropriate?
a) CV and range
b) arithmetic mean and standard deviation
c) interquartile range and median
d) variance and interquartile rangs
7. Given a normally distributed population with a mean of 80 and a variance of l00, we
know that the distribution of sample means computed from samples of size 25 from
that population will have a mean of _____ and a standard error of _____.
a) 80,
b) 80,
c) l00,
d) 80,
l0
2
25
l0
8. In sampling from a large population with sigma = 20, the standard error of the mean
is found to be 2. The size of the sample used is:
a) 100
b) 40
c) 10
d) 20
9. The width of a confidence interval estimate for a proportion will be
a) narrower when the sample proportion is 0.10 than when the sample proportion is
0.45
b) wider for 90% confidence than for 95% confidence.
c) narrowest when the sample proportion is 0.5.
d) narrower for a sample size of 50 than for a sample size of 100.
10. In a survey of 3200 T.V. viewers, 20% said they watch network news programs.
Find the standard error for the sample proportion.
a) 0.0071
b) 0.0865
c) 0.0721
d)0.0142
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Question # 2 : For each question in this section, indicate whether the sentence is
true or false.( 10 points).
1.
( T ) The amount of time a student spend studying for an exam is an example of a
continuous variable.
2. ( T )A point estimator is a function of the random sample used to make inferences
about the value of an unknown population parameter.
3. ( T
)confidence interval provides a range of values that, with a certain level of
confidence, contains the population parameter of interest
4. ( F ) Given a sample mean of 2.1 and a population standard deviation of 0.7 from a
sample of 10 data points, a 90% confidence interval will have a width of 2.36
5. ( F ) Suppose you are constructing a confidence interval for the population mean.
For a given confidence level and standard deviation, the width of the interval
is wider for a larger sample size.
6. ( T ) The coefficient of variation measures variability in a data set relative to
the size of the arithmetic mean.
7. ( F ) The standard error of the sample mean is affected by the confidence level .
8. ( T)The central limit theorem is important in statistics because for a large n, it says
the sampling distribution of the sample mean is approximately normal,
regardless of the shape of the population
9. ( F
)The student's t distribution is used to construct confidence intervals for the
population mean when the population standard deviation is known
10. ( F)The middle 50% of the normal distribution, is equal to one standard deviation
Question #3: (10 Points)
1.(2 points)The amount of pyridoxine (in grams) per multiple vitamin is normally
distributed with   110 grams and   25 grams. A random sample of 25 vitamins
is to be selected. What is the probability that the sample mean will be greater than 100
gram?
P(x>100)=p(z>(100-110)/(25/sqrt(25))= p(z>-2) = 1-p(z<-2)
= 1-0.0228 = 0.9772
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2. (3 points)According to a survey, only 15% of customers who visited the web site of a
major retail store made a purchase . Random samples of size 50 are selected, 90% of
the samples will have more than what percentage of customers who will make a
purchase after visiting the web site?
p ( P  p1 )  0.90
p ( z  z1 )  0.9 ,
where z1 
p ( z  z1 )  0.10, z1   1.28 
p1  0.15
0.15 * (1  0.15) / 50
p1  0.15
0.15 * (1  0.15) / 50
p1  0.085363  8.536%
3. (2 points)The county clerk wants to estimate the proportion of retired voters who will
need special election facilities. The clerk wants to find a 95% confidence interval for
the population proportion which extends at most 0.07 to either side of the sample
proportion. How large a sample must be taken to assure these conditions are met?
Z
π (1  π ) (1.96) 2 (0.5)(1  0.5)
n  /2 2

 196
e
(0.07) 2
2
4. (3 points) A hotel chain wants to estimate the average number of rooms rented daily in
each month. The population of rooms rented daily is assumed to be normally
distributed for each month with a standard deviation of 24 rooms. During January, a
sample of 16 days has a sample mean of 48 rooms. This information is used to
calculate an interval estimate for the population mean to be from 40 to 56 rooms.
What is the level of confidence of this interval?
e  Z / 2
σ
n
,
8Z
24
16
, Z  1.33 C.I  81.76
you may use the following formulae:
4
n
x
 xi
i 1
n
N
1 n
2
, S
 xi  x  ,

n  1 i 1
x   ,  x 


, p   ,  p 
n
s
p(1  p)
, xt
pz
n
n
5
X
i 1
N
 1   
n
,
i
, 2 
1 N
2
 xi   

N i 1
Z 2 p (1  p)
, n
e2
xz

n
n
Z  / 22 σ2
e2
6
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