MBA I Semester Supplementary Examinations December/January 2018/19

BUSINESS STATISTICS

(For students admitted in 2014 (LC), 2015 & 2016 only)

Time: 3 hours Max. Marks: 60

SECTION -A

(Answer the following: (05 X 10 = 50 Marks)

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1. Enumerate the methods of measuring dispersion and state the characteristics of a good measure of dispersion.
   OR
   The coefficient of variation of wages of male workers and female workers are 55% and 70% respectively, while the standard deviations are 22.0 and 15.4 respectively. Calculate the overall average wages of all workers given that 80% of the workers are male.
2. State the properties of Karl Pearson's coefficient of correlation and explain how would you interpret the value of r with a suitable example.
   OR
   

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   Find the coefficient of correlation by Karl Pearson's method from the following table.
   X 6 2 10 4 8
   Y 9 11 ? 8 7
   Arithmetic means of X and Y are 6 and 8 respectively.
3. State the important characteristics and properties of binomial distribution. Under what conditions can a binomial distribution be applied?
   

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   OR
   The following table shows the distribution of number of faulty units produced in a single shift in a factory. The data is for 400 shifts.
   No. of faults 0 1 2 3 4
   No. of shifts 138 161 69 27 5
   Fit a Poisson distribution to the data.

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4. In a large city A, 20% of the random sample of 1000 school children had defective eyesight. In another large city B, 15% of a random sample of 2000 children had the same defect. Is this difference between two proportions significant? Obtain 95% confidence limits for the difference in the population proportions.
   OR
   Two random samples were drawn from two normal populations and their values are:
   A 66 67 75 76 82 84 88 90 92
   B 64 66 74 78 82 85 87 92 93 95 97
   

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   Test whether the two populations have the same variance at 5% level of significance.
   (F = 4.30 at 5% level for v1 = 10 and v2 = 8)
5. The number of car accidents in a city was found as 20, 17, 12, 6, 7, 15, 8, 5, 16 and 14 per month. Use Chi-square test to check whether these frequencies are in agreement with the belief that occurrence of accidents was the same during the 10 month period. Test at 5% level of significance.
   OR
   In a survey of 200 girls of which 40% were intelligent, 30% had uneducated fathers, while 20% of the unintelligent girls had educated fathers. Do these figures support the hypothesis that educated fathers have intelligent girls? Test at 5% level of significance. (Table value of x² = 3.84)

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SECTION -B

(Compulsory question, 01 X 10 = 10 Marks)

1. Case Study:
   In a certain factory production can be accomplished by four different workers on 5 different types of machines. A sample study, in context of a two-way design without repeated values, is being made with two-fold objectives of examining whether the four workers differ with respect to mean productivity and whether the mean productivity is the same for the 5 different machines. The researcher involved in this study reports while analyzing the data as under.
   (i) Sum of squares for variance between machines = 35.2
   (ii) Sum of squares for variance between work man = 53.8
   

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   (iii) Sum of square for total variance = 174.2
   Set up ANOVA table for the given information and draw the inference about variances at 5% level of significance (Table value F = 2.53)

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