Question Bank-Business Statistics

	Random samples drawn from two places gave the following data relating to the heights of adult males:
	Place A Place B Mean height (inches) 68.50 68.58 Standard Deviation (inches) 2.50 3.00 Sample size 1200 1500
	Test at 5% level of significance that the mean height is the same for adults in two places.
Q.2.	A manufacturer of ball point pens claims that a certain pen he manufactures has a mean writing life of 400 pages with a standard deviation of 20 pages. A purchasing agent selects a sample of 100 pens and puts them or test. The mean writing life for the sample was 390 pages. Should the purchasing agent reject the manufacturer's claim at 5% level.
Q.3.	Below are given the gain in weights (in lbs.) of pigs fed on two diets A and B.
	Diet A: 25 32 30 34 24 14 32 24 30 31 35 25 Diet B: 44 34 22 10 47 31 40 30 32 35 18 21 35 29
	Test if the two diets differ significantly as regards their effect on increase in weight.
Q.4.	A random sample of size 16 has 53 as mean. The sum for squares of the deviations taken from mean is 150. Can this sample be regarded as taken from the population having 56 as mean? (a = 5%).
Q.5.	In 120 throws of single die the following distribution of faces was obtained: Faces: 1 2 3 4 5 6 Freq.: 30 25 18 10 22 15 Test whether results constitute a repartition of equal probability for each face.
Q.6.	In a recent diet survey the following results were obtained in a city: Community A Community B No. of families taking tea 1,236 164 No. of families not taking tea 564 36 Test whether there is any significant difference between the two communities in the matter of taking tea?
Q.7.	The standard deviations calculated from two random samples of size 9 and 13 are 4 and 3.8 respectively. On the samples be regarded as drawn from normal population with the same standard deviation?

Correlation and Regression Analysis

Q.1. Compute the coefficient of correlation from the following:

data	X:	09	18	18	20	20	23
	Y:	23	33	23	42	29	32

Q.2. Compute the rank correlation coefficient from the following data:

Section A:	115	109	112	87	98	120	100	98	118
Section B:	75	73	85	70	76	65	82	73	80

Q.3. Find , , , r if .

5X + 7Y – 22 = 0 (1)

6X + 2Y – 20 = 0 (2)

Q.4. If r = 0.8

	X (Rs. Lakhs)	Y (Rs. Lakhs)
Mean	20	100
S.D.	3	12

(i) Find the two regression lines.

(ii) X = ? if Y = Rs. 120.

Time Series

Q.1. The following table shows the number of sales man working for a certain concern:

Year:	1998	1999	2000	2001	2002	2003
Number:	28	38	46	40	56	60

By least-square method.

Q.2. Determine straight line trend by semi-average method for the following time series data:

Year:	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990
Production (,000 units):	18	25	21	15	26	31	30	20	35	32	23

Measures of Central Tendency:

Q.1. Determine Mean, Median and mode from the following table:

Marks (Less Than):	10	20	30	40	50	60	70	80
No. of Students:	25	40	60	75	95	125	190	240

Q.2. Find the missing frequency in the following distribution whose mean is 27:

Class:	0-10	10-20	20-30	30-40	40-50
Frequency:	5	?	15	16	6

Measures of Dispersion

Q.1. Find the S.D. and C.V. from the following data:

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of Students:	10	15	25	25	10	10	5

Q.2. The runs scored by two batsman A and B in 9 consecutive matches are given below:

A:	85	20	62	28	74	5	69	4	13
B:	72	4	15	30	59	15	49	27	26

Which of the batsmen is more consistent?

Probability and Theoretical Probability Distributions:

Q.1. The average monthly sales of 5000 firms in an industry in Banglore are normally distributed with mean Rs. 36000 and S.D. Rs. 10000. Find

(i) the number of firms with sales over Rs. 40,000

(ii) the percentage of firms with sales between Rs. 38,500 and Rs. 41,000.

(iii) the number of firms with sales between Rs. 30,000 and Rs. 40,000.

Q.2. If Z is a standard normal variable. Find the following probabilities:

(i) (ii) (iii)

Measures of Control Tendency and Measures of Dispersion

Q.1. "Statistics plays an important role not only in the study of economics and commerce, but also in managerial decision-making." Explain briefly.

Q.2. Write short notes on:

(a) Measures of Central Tendency

(b) Measures of Dispersion

Q.3. Discuss the merits and demerits of mode.

Time Series Correlation & Regression Analysis Index Numbers

Q.1. Define time series. Explain the components of time series with suitable examples.

Q.2. Give the models (Additive & Multiplicative) of decomposition of analysis of time series.

Q.3. Define correlation and Regression. Give the difference between them. Also write the application of both.

Q.4. Define Index Numbers. Give the uses of Index numbers. What are the problems in construction of Index numbers? Discuss in detail.

Probability, Probability Theoretical Distribution

Q.1. What is addition and multiplication theorem of Probability? Discuss.

Q.2. Define Bayes Theorem.

Q.3. Write short notes on:

(a) Binomial Distribution

(b) Poisson Distribution

Estimation Theory and Hypothesis Testing

Q.1. Write the procedure for testing of hypothesis.

Q.2. Difference between sample survey and population (Census) Survey.

Q.3. Difference between parameters and statistic.

Q.4. Define two-types of errors.

Q.5. Null and Alternative Hypothesis.

Q.6. Level of significance and Degrees of Freedom.