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

If the two regression coefficients are 0·8 and 0.6, the coefficient of correlation is -0.69.

The probability of getting a sum of 8 or more in a simple throw with two dice is 15/36.

If for a binomial distribution the mean is 4 and the variance is then the number of trials is equal to 16.

A 95% confidence interval is smaller than a 99% confidence interval.

For a population of 5 households, using circular systematic sampling, at most 10 samples of sample size 2 can be selected.

An enquiry into 50 families to study the relationship between expenditure on accommodation, RS and expenditure on food and entertainment, RS Y gave the following results

<img src='./qimages/10437-2a.jpg'>

Estimate the expenditure on food and entertainment when the expenditure on accommodation is RS 200.

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. Find the number of boys and the number of girls in the class.

The data on chicks born in a farm are given below for 60 days. Compute the mean and standard deviation by doing a frequency distribution:

1,0,3.
(Take class width

From the following data, calculate the 4-yearly moving average and determine the trend values:

<img src='./qimages/10437-3a.jpg'>

There are 100 fields in a village sown with wheat and each is divided into 10 plots of equal size. Out of 100 fields, 5 fields are selected by without replacement simple random sampling method. Again, from each selected field, 3 plots are chosen by without replacement simple random sampling method. The yield in kg/plot recorded is as given in the following table

<img src='./qimages/10437-3b.jpg'>

Estimate the quantities and

=0.50, =0·40 and P(A U 0.70, find and U where AC is the complement of A. State whether A and B are independent. Justify your answer.

The mean and variance of a binomial distribution are 3 and respectively. Find the probability that the variate takes values less than or equal to 2.

The hobbing operation is an important step in gear cutting. Defects occur during the hobbing and on quality check they are recorded. The defects may be the presence of burr, nicks, pits, chamfer angle defect, lead error defect or profile error defect. The data on these were collected for 10 gears per day, that were cut. Draw a suitable control chart and interpret.

<img src='./qimages/10437-4c.jpg'>

In a random sample of 100 articles taken from a large batch of articles, 10 are found to be defective. Obtain a and 99% confidence interval for the true proportion of defectives in each batch.

Cite two situations where systematic sampling is appropriate. Explain how it is different from stratified sampling. Justify.

A random sample of male employees is taken at the end of a year and the mean number of hours of absenteeism for the year is found to be 63 hours. A similar sample of 50 female employees has a mean of 66 hours. Could these samples be drawn from a population with the same mean and standard deviation of 10 hours (Use a

Two sets of ten students selected at random from a college were taken; one was given memory test as they were and the other set was given a memory test after two weeks' training and the scores are given below

<img src='./qimages/10437-6a.jpg'>

Do you think that there is any significant effect due to training? Justify.
Use a 0·05. [You Play like to use the values given at the end of the question paper.]

Consider a simple random sample of two households from a population of five households having monthly income (in RS) as follows

<img src='./qimages/10437-6b.jpg'>

Enumerate all possible samples of size 2 and show that the sample mean gives an unbiased estimate of population mean.

There are three engineers doing four jobs. The time required to do the jobs is recorded. Find whether the engineers play a significant role or not. Also, find the job which takes most of the time for the engineers to do.

<img src='./qimages/10437-7a.jpg'>

Use a

The average monthly sales of 5000 firms are normally distributed. Its mean and standard deviation are RS 36,000 and RS 10,000, respectively. Find

the number of firms the sales of which are over RS 40,000.

the percentage of firms, the sales of which will be between RS 38,500 and RS 41,000.

<img src='./qimages/10437-Table.jpg'>