LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Com. DEGREE EXAMINATION – COMMERCE

KP 39

FIRST SEMESTER – April 2009

CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

 

Date & Time: 30/04/2009 / 1:00 – 4:00       Dept. No.                                                       Max. : 100 Marks

 

 

SECTION: A

Answer All Questions:                                                                                       10 x 2 = 20

 

• Indicate whether the following are True or False:
  1. A listing of all population units is called a frame.
  2. One of the biggest problems in survey is that of non – response.
• What is a questionnaire?
• What is Skewness?
• Indicate whether the following are True or False:
  1. In a symmetrical distribution, Mean = Median = Mode.
  2. β2 is a measure of Kurtosis.
• What are the components of Time Series?
• Three perfect coins are tossed together. What is the probability of getting at least one head?
• What is meant by theoretical frequency distribution?
• What do you mean by the statistical quality control charts?
• What are non parametric tests?
• Define Type I and Type II errors.

 

SECTION – B

Answer any five only:                                                                              5 x 8 = 40

 

• What is a Control Chart? Show a typical Control Chart. How are Control Charts for Mean and Range constructed when Standard are given?

 

• What are the basic conditions for the application of Chi – Square test?

 

13) Write short notes on the following terms

• Mutually exclusive events
• Independent and dependent events
• Equally likely events
• Complementary events

 

• Ten students are selected at random from a college and their heights are found to be 100, 104, 106, 110, 118, 120,122,124,126 and 128 cms. In the light of these data discuss the assumption that the mean height of the students of the college is 110cm.

The table value of t at 5% level for 8 df is 2.306 and for 9 df is 2.262 and 10 df is 2.228 for a two tailed test.

 

• The following data is collected on two characteristics:

Particulars                   Smokers          Non – Smokers

Literate                             83                           57

Illiterate                            45                           68

Based on this can you say that there is no relation between the habit of smoking and literacy.

 

16) The following table relates to the tourist arrivals (in millions) during 1997 to 2003

India:

Years:                         1997    1998    1999    2000    2001    2002    2003

Tourists arrivals:           18        20        23        25        24        28        30

(In millions)

 

Fit a straight line trend by the method of least squares and estimate the number of

tourists that would arrive in the year 2009.

 

17) The following are some of the particulars of the distribution of weight of boys

and girls in a class:

Boys                            Girls

Number                                   100                              50

Mean Weight                          60 Kg                         45 Kg

Variance                                  9                                 4

Find the standard deviation of the combined data.

Which of the two distributions is more variable?

 

• The following data is relating to the units produced per day by 4 workers in 5 machines of different types. Test whether the four workers differ in terms of mean productivity and test whether the mean productivity is the same for the five different machines. Perform Two Way

Workers	Machine Type
	1	2	3	4	5
1	10	9	8	12	10
2	11	9	8	12	10
3	13	10	9	10	11
4	14	9	8	12	12

 

SECTION – C

Answer any two only:                                                                                  2 x 20 = 40

 

• The following are the numbers of hours which 10 students studied for an examination and the scores they obtained:

No. of hours Studied (x)	8	5	11	13	10	5	18	15	2	8
Score (y)	56	44	79	72	70	54	94	85	33	65

Calculate rank correlation; also test at  0.01 level of significance whether the value obtained is significant.

 

• School children taking coaching in three private schools A,B and C secure the following scores out of 100.

No of Children	1	2	3	4	5	6	7	8	9	10
School – A	33	38	39	48	58	70	61	41	45	49
School – B	32	15	87	32	22	63	56	57	44	—
School – C	55	68	27	88	46	52	76	—	—	—

Test the hypothesis that the students in the three private schools have identical distribution of scores at significance level at 1 %. Apply H test.

 

• The life time of electric bulbs for a random sample of 10 from a large consignment gave the following data:

Item	1	2	3	4	5	6	7	8	9	10
Life in ‘000 hours	4.2	4.6	3.9	4.1	5.2	3.8	3.9	4.3	4.4	5.6

Can we accept the hypothesis that the average life time of bulbs is 4000 hours.

 

 

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