Assignment Task :

 

1. State whether the following statements are true or false. Give a brief justification.

a) If two variables are independent, then the coefficient of correlation between them is 1. 

b) The mean of a binomial distribution is 10 and the standard deviation is 4. 

c) Simple random sampling is done by using a random number where the probability of drawing a digit is 0.1. 

d) The number of six-digit telephone numbers generated with distinct digits is (9)6. 

e) If 25 is subtracted from each value of X and Y and then divided by 10, the new yx b′ is 2.5 times of yx b , where yx b is a regression coefficient of Y on X. 

 

2. a) The mean and standard deviation of a characteristic of 100 items were found to be 60 and 10, respectively. At the time of calculations, two items were wrongly taken as 5and 45 instead of 30 and 20. Calculate the corrected mean and standard deviation. (3) 

b) A person speaks the truth 3 out of 4 times. A die is thrown. She reports that there is five. What the chance that there were five? (3) 

c) In a normal distribution, 10% of the items are over 125 and 35% are under 60. Find the mean and standard deviation of the distribution.

4. a) Of the 200 people selected randomly from a large city, 120 were found to be in favor of more liberal traffic laws. Obtain a 95% confidence interval of the proportion of the people in the city who favor more liberal traffic laws.

5. a) The number of defects in 20 carpets are given as 2,0,4,1,0,8,0,1,2,0,6,0,2,1,0,3,2,1, 0,2. Find the suitable control limits and plot them on the graph and interpret the results.

b) The lifetime of 10 electric bulbs (in thousands of hours) are as follows: 2, 3, 2, 3, 2, 3, 4, 4, 3, 4 Determine an unbiased estimate of the population mean and standard deviation. 

6. a) A sample of size 3 is to be selected from a population of 10 households. List all the 

possible samples by: 

i) Linear Systematic Sampling

ii) Circular Systematic Sampling 

 

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  • Posted on : November 27th, 2018

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