HARAMAYA UNIVERSITY
COLLEGE OF COMPUTING AND INFORMATICS
DEPARTMENT OF STATISTICS
INTRODUCTION TO STATISTICS ASSIGNMENT
Name: _______________________________________________
Id №: ________________________________________________
Department: __________________________________________
Center: ______________________________
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Part-I: Indicate whether the statement is true or false.
1. In a sample of 1000 students in a university, 125 of them or 12.5% are biology majors.
The 12.5% is an example of statistical inference.
2. The number of students living off-campus is an example of a discrete random variable.
3. The time required to assemble a computer is an example of a discrete random variable.
Part -II: Identify the choice that best completes the statement or answers the question.
4. Which of the following is not the goal of descriptive statistics?
a) Summarizing data
b) Displaying aspects of the collected data
c) Reporting numerical findings
d) Estimating characteristics of the population based on a sample
e) None of these
5. Which of the following statements is correct?
a) The range is a measure of central tendency.
b) The median is a measure of dispersion.
c) For a symmetric distribution, the mean is equal to the median.
d) For a skewed distribution, the variance is a negative number.
e) The variance is a measure of central tendency.
6. Suppose P (A) = 0.4, P (B) = 0.3, and P (A∩B) = 0. Which of the following statements
correctly defines the relationship between events A and B?
a) Events A and B are independent, but not mutually exclusive.
b) Events A and B are mutually exclusive, but not independent.
c) Events A and B are neither independent nor mutually exclusive.
d) Events A and B are both independent and mutually exclusive.
e) None of these.
7. Which of the following statements regarding a binomial experiment is false, where n is
the number of trials, and p is the probability of success in each trial?
a) The n trials are independent.
b) The standard deviation is np (1- p).
c) The mean is np.
d) There are only two possible outcomes.
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8. Which probability distribution is appropriate when the events of interest occur randomly,
independently of one another, and rarely?
a) Binomial distribution
b) Poisson distribution
c) Hypergeometric distribution
d) Any discrete probability distribution.
9. A 99% confidence interval estimate for a population mean µ is determined to be 85.58 to
96.62. If the confidence level is reduced to 90%, the confidence interval for µ:
a) Becomes wider
b) Remains the same
c) Becomes narrower
d) Becomes wider on the left but remains the same on the right
e) None of these
Part -III: You must carefully and completely show your work step by step.
1. In a certain investigation, 460 persons were involved in the study, and based on an enquiry
on their age, it was known that 75% of them were 22 or more. The following frequency
distribution shows the age composition of the persons under study.
Mid-age in years
13 18 23 28
Number of persons 24 f1
33 38 43 48
90 122 f2
56 20 33
a) Find the median and modal life of condensers and interpret them.
b) Find the values of all quartiles.
c) Compute the 5th decile, 25th percentile, 50th percentile and the 75th percentile and
interpret the results.
d) Find variance and standard deviation of the data.
10. Let y be a normal random variable with µ = 100 and σ = 8. Find the following
probabilities.
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a) P( y > 100)
b) P ( y < 110)
c) P ( 100 < y < 108)
11. A university dean is interested in determining the proportion of students who receive
some sort of financial aid. Rather than examine the records for all students, the dean
randomly selects 200 students and finds that 118 of them are receiving financial aid. Use
a 99% confidence interval to estimate the true proportion of students on financial aid.
12. A local juice manufacturer distributes juice in bottles labeled 32 ounces. A government
agency thinks that the company is cheating its customers. The agency selects 35 of these
bottles, measures their contents, and obtains a sample mean of 31.7 ounces with a
standard deviation of 0.70 ounce. Use a 0.01 significance level to test the agency's claim
that the company is cheating its customers.
13. Given the following data on supply (X) and sales (Y) of a certain commodity.
X
60
62
65
70
73
75
71
Y
10
11
13
15
16
19
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a) Estimate the regression equation supply on sales.
b) Interpret the estimated coefficients (the slope and intercept).
c) Calculate the correlation coefficient between supply and sales, and interpret it.
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