A random sample of size 50 with mean 67.9 is drawn from a normal population. If it is known that the standard error of the sample \(\sqrt { 0.7 } \) , find 95% confidence interval for the population mean.

Out of 1000 T.V. viewers, 320 watched a particular programme. Calculate the standard error.

Out of 1500 school students, a sample of 150 selected to test the accuracy of solving a problem in B.M. and of them 10 did a mistake. Calculate the standard error of sample proportion.

A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

The income distribution of the population of a village has a mean of Rs. 6000 and a variance of Rs. 32,400. Could a sample of 64 persons with a mean income of Rs. 5950 belong to this population. (Test at 1% level of significance).