1. State whether the following statements are True or False. Give brief justification. The mean of a binomial distribution is and the standard deviation is 4. If two variables are independent, then the coefficient of correlation between them is 1. Simple random sampling is done by using random number tables, where the probability of drawing a digit is 0·1.
The area under the curve of a standard normal distribution between 0 and infinity is 1.
The chi-square test is a non-parametric test.

2. The quarterly profits and sales (in lakhs of RS) of six appliance firms are as follows: <img src='./qimages/8331-2a.jpg'> Construct the scatter diagram.
Which variable (profit or sale) is suggested as the dependent variable?

(iii) Compute the sample regression line.
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 5 and 45 instead of 30 and 20. Calculate the corrected mean and standard deviation.

3. A random sample of 200 villages was taken from Gorakhpur district and the average
population per village was found to be 485 with a standard deviation of 50. Another random sample of 200 villages' from the same district gave an average population of 510 per village with a standard deviation of 40. Is the difference between averages of the two samples statistically significant at level. The mean and variance of a Poisson distribution are both 3. Find the probability when the variate takes values less than or equal to 2.

4. From the data given below about the treatment of 500 patients suffering from a disease, find out whether the new treatment is superior to the conventional treatment using appropriate tests <img src='./qimages/8331-4a.jpg'>
Define Sampling and explain what advantages it has over the census approach. Explain with a situation.

5. The mean and standard deviation computed from a large sample are 10 and respectively. Use the normal distribution approximation to answer the following:
What percentage of the measurements lie between 7 and 13
What percentage of the measurements are greater than 16 Each of four chemists are testing 5 specimens of fibre and recording the tensile strength in kg of each fibre. Unfortunately, complete data could not be collected and the data is as given below <img src='./qimages/8331-5b.jpg'>

Do the chemists perform equivalently? Use
<img src='./qimages/8331-5b value.jpg'>

6. For the following series of observations, calculate the trend values by the exponential smoothing method with ao 10,000 and weight 0·3 <img src='./qimages/8331-6a.jpg'>

Interpret the result.
Suppose from a total of 120 apple trees, 5 clusters of 4 trees each are selected and the yield (in kg) is recorded below <img src='./qimages/8331-6b.jpg'>

Estimate the average yield per tree and its standard error.

7. Suppose three small towns, under study, have population N1 50000, N2 30000 and N3= 40000, respectively. A stratified random sample is to be taken with a total sample size of n 500. Determine the sample size to be taken from each town individually using the method of proportional, and

(ii) optimal allocation. Past experience indicates that S1 S2 =15 and S3 =20.
A simple random sample of size 100 has mean 15 and population variance 25. Find an interval estimate of the population mean with a confidence level of 99% and 95%. Some values for use, if required. Table Values:

<br><br> <img src='./qimages/8331-7b.jpg'>