1. A genetics law says that children having one parent of blood group M and the other parent of blood group N will always be one if the three blood groups M, MN, N and that the average number of children in these groups will be in the ratio 1 : 2 : 1. The report on an experiment states as follows: “Of 162 children having one M parent, and one N parent, 28.4% were found to be of group M, 42% of group MN and the rest of the group N.” Do the data in the report conform to the expected genetic ratio 1 : 2 : 1?

2. The following table gives the count of yeast cells in square if a cyclometer. A square millimeter is divided into 400 equal squares and the number of these squares containing 0, 1, 2, … cells are recorded: No. of Cells| 0| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11| 12| 13| 14| 15| 16| Frequency| 0| 20| 43| 53| 86| 70| 54| 37| 18| 10| 5| 2| 2| 0| 0| 0| 0|

Fit a Poisson distribution to the data and test the goodness of fit. 3. A drug manufacturer has installed a machine which automatically fills 5 gm of drug in each phial. A random sample of fills was taken and it was found to contain 5.02 gm on an average in a phial. The standard deviation of the sample was 0.002 gms. Test at 5% level of significance if the adjustment in the machine is in order. (Ans. tcal = 33.33, H0 is rejected.) 4. The heights of 10 males of a given locality are found to be 70, 67, 62, 68,61, 68, 70, 64, 64, 66 inches. Is it reasonable to believe that the average height is greater than 64 inches? Test at 5% significance level, assuming that for 9 degrees of freedom P(t > 1.83) = 0.05. 5. Eleven sales executive trainees are assigned selling jobs right after their recruitment. After a fortnight they are withdrawn from their field duties and given a month’s training for executive sales. Sales executed by them in thousands of rupees before and after the training, in the same period are listed below: BT| 23| 20| 19| 21| 18| 20| 18| 17| 23| 16| 19| AT| 24| 19| 21| 18| 20| 22| 20| 20| 23| 20| 27| Do these data indicate that the training has contributed to their performance? (Ans.: tcal = 2.14, accept H0) 6. In a sample of 1000 people in Maharashtra, 540 are rice eaters and the rest are wheat eaters. Can we assume that both rice and wheat are equally popular in this State at 1% level of significance? (Ans.: Zcal = 2.532, hence H0 is accepted at 1% level of significance thus rice and wheat are equally popular in the state of Maharashtra) 7. Random samples of 400 men and 600 women were asked whether they would like to have a flyover near their residence. 200 men and 325 women were in favour of the proposal. Test the hypothesis that proportions of men and women in favour of the proposal are same against that they are not, at 5% level. (Ans.: Zcal = -1.269, accept H0 at 5% level of significance hence proportions of men and women in favour of the proposal are same.) 8. An insurance agent has claimed that the average age of policyholders who insure through him is less than average for all agents, which is 30.5 years. A random sample of 100 policyholders who had insured through him gave the following age distribution: Age last birthday| 16-20| 21-25| 26-30| 31-35| 36-40| No. Of persons| 12| 22| 20| 30| 16|

Calculate the arithmetic mean and standard deviation of this distribution and use these values to test his claim at 5% level of significance. You are given that Z (1.645) = 0.95. (Ans.: Zcal = -2.681, reject H0 at 5% level of significance hence the insurance agent’s claim that the average of policyholders who insure through him is less than the average for all agents, is valid) 9. The means of two single large samples of 1000 and 2000 members are 67.5 inches and 68.0 inches respectively. Can the samples be regarded as drawn from the same population of standard deviation 2.5 inches? (Test at 5% level of...