MBA I Semester I

Quantitative Analysis – I Sample Paper

Time: Total Marks: 70 [Note: The Question Paper has five Questions of 14 marks each. It is compulsory to attempt all the questions.]

Q.1. Answer all the following multiple choice questions: (14) 1. As the number of observations and classes increase, the shape of a frequency polygon

(a) Tends to become increasing smooth

(b) Tends to become jagged

(c) Stays the same

(d) Varies if data become more reliable

2. Continuous data are different from discrete data in that

(a) Discrete data classes are represented by fractions

(b) Continuous data classes may be presented by fractions

(c) Continuous data take on only whole numbers

(d) Discrete data can take on any real number

3. The mode has all of the following disadvantages except

(a) A data set may have no modal value

(b) Every value in a data set may be a mode

(c) A multimodal data set is difficult to analyze

(d) The mode is unduly affected by extreme values

4. Which of the following is an example of a relative measure of dispersion?

(a) Standard deviation

(b) Variance

(c) Coefficient of variation

(d) All of these

(e) (a) and (b), but not (c)

5. If P(A or B) = P(A), then

(a) A and B are mutually exclusive

(b) The Venn diagram areas for A and B overlap

(c) P(A) + P(B) is the joint probability of A and B

(d) None of the above

6. If we sum all the probabilities of the conditional events in which the event A occurs while under statistical

dependence, the result is

(a) The marginal probability of A

(b) The joint probability of A

(c) The conditional probability of A

(d) None of these

7. For a given binomial distribution with n fixed, if p< 0.5, then:

(a) The Poisson distribution will provide a good approximation

(b) The Poisson distribution will provide a bad approximation

(c) The Poisson distribution will be skewed left

(d) The Poisson distribution will be skewed right

(e) The Poisson distribution will be symmetric

8. For a normal curve with µ=55 and σ=10, how much area will be found under the curve to the right of the value 55?

(a) 1.0

(b) 0.68

(c) 0.5

(d) 0.32

(e) Cannot be determined from the information given

9. The central limit theorem

(a) Requires some knowledge of the frequency distribution

(b) Permits us to use sample statistics to make inferences about population parameters

(c) Relates the shape of a sampling distribution of the mean to the mean of the sample

(d) Requires a sample to contain fewer than 30 observations

10. When a null hypothesis is accepted, it is possible that:

(a) A correct decision has been made

(b) A Type-I error has been made

(c) Both (a) and (b) have occurred

(d) Neither (a) nor (b) has occurred

(e) None of these

11. For which of the following is a two-sample test not appropriate?

(a) Seeing whether the proportions of childless couples and couples with children who buy sports cars

are different

(b) Seeing whether the mean beer consumption is higher in Germany than in France

(c) Testing whether there are more men than women in Alaska

(d) Deciding whether average attendance at major league baseball games is the same in Los Angeles and

San Francisco

12. Which of the following tests could be based on the normal distribution?

(a) Difference between independent means

(b) Difference between dependent means

(c) Difference between proportions

(d) All of the above

(e) (a) and (c) but not (b)

13. A chi-square value can never be negative because:

(a) Differences between expected and observed frequencies are squared

(b) A negative value would mean that the observed frequencies were negative

(c) The absolute value of the differences is computed

(d) None of these

(e) (a) and (b) but not (c)

14. Suppose it is calculated that a=4 and b=2 for a particular estimating line with one independent variable. If

the independent variable has a value of 2, what value should be expected for the dependent variable?

(a) 8

(b) 10

(c) -1

(d) 0

Q.2.

(A) Explain the following short terms with example.(Any TWO)

(7)

1. Mutually exclusive events

2. Skewness and Kurtosis

3. Type-I and Type-II error

4. Conditional Probability

(B) Define Statistics. Explain two business applications of statistics. (7)

OR

(B) Describe briefly random and non random sampling methods (7)

Q.3.

(A) What is Regression? Explain the use of Regression in Business Analysis. (7)

(B) Suppose inter-arrival times at a hospital emergency room during a weekday are exponentially

distributed, with an average inter-arrival time of 9 minutes. If the arrivals are Poisson distributed, what would

the average number of arrivals per hour be? What is the probability that less than 5 minutes will elapse between

any two arrivals? What is the probability that more than 7 minutes will elapse between any two arrivals?

(7)

OR

Q.3.

(A) Discuss the levels of Data measurement (7)

(B) A study of pollutants showed that certain industrial emissions should not exceed 2.5 parts per million.

You believe a particular company may be exceeding this average. To test this supposition, you randomly take a

sample of nine air tests. The sample average is 3.4 parts per million, with a sample standard deviation of 0.6.

Does this result provide enough evidence for you to conclude that the company is exceeding the safe limit? Use

α=0.01. Assume emissions are normally distributed. (7)

Q.4.

(A) What is hypothesis? Explain the types of hypothesis and also the process of hypothesis testing (7)

(B) Are the types of professional jobs held in the computing industry independent of the number of years a

person has worked in the industry? Suppose 246 workers are interviewed. Use the results obtained to determine

whether type of professional job held in the computer industry is independent of years worked in the industry.

Let α=0.01 (7)

Professional Position

Years

Manager Programmer Operator Systems Analyst

0-3 6 37 11 13

4-8 28 16 23 24

More than 8 47 10 12 19

OR

Q.4.

(A) Explain Uniform, Exponential and Normal distributions. (7)

(B) Determine the sample size necessary under the following conditions: (7)

a. To estimate µ with σ=44, E=3 and 95% confidence

b. to estimate µ with a range of values from 20 to 88 with E=2 and 90% confidence

c. to estimate p with E=0.04 and 98% confidence

Q.5. Solve the following Case study. (14) One of the key measures of service quality of any organization is the speed with which it responds to customer

complaints. A direct selling organization specializing in vacuum cleaner and water filters has undergone major

expansion plans in the past several years. The section handling water filters both for domestic as well as

industrial purpose had expanded from 4 installation crews to an installation supervisor, a measurer and 15

installation crews.

During the past year after the expansion was completely put into the place there were 15 complaints

concerning water filter installation. The following data gives the no. of days between receipt of the complaint

and the resolution of complaint.

2 4 5 7 1 6 8 9 10 12

13 5 7 8 5 4 3 2 8 12

1 5 4 2 3 7 8 10 11 4

5 6 2 3 1 8 9 9 10 5

8 7 1 10 12 11 1 1 2 3

The installation supervisor claims that the mean no. of days between receipt and resolution of

complaints is 8 days. Answer the following questions.

a. Prepare the null and alternative hypothesis.

b. Is the claim made by installation supervisor true? What assumption needs to be made in this case? Solve

through hypothesis testing.

OR

Q.5. Solve the following Case study. (14) An electronic company has two suppliers for wires for their printed circuit boards (PCB). Lately there have

been reports of quality problems from the production department about the breaking strength of wires. To test

the performance of the individual suppliers, two samples of size 5 each were taken from two lots-one of

supplier A and one of supplier B. The results are

A: 290 304 296 312 325

B: 275 325 350 305 375

Answer the following question:

a. Find mean and median for both the suppliers

b. Find sample variance, sample standard deviation, mean absolute deviation for both the suppliers

c. Use Coefficient of Variation to test which supplier is more consistent.

Prepared by: Rinal Shah (LJIMS)