Answer the following questions a Explain what the sampling d

Answer the following questions.

a) Explain what the sampling distribution of the mean is and why it is needed to test hypotheses about the mean and construct confidence intervals for the mean. What is the standard error of the mean? What distribution does the sampling distribution of the mean follows approximately?

b) Why is hypothesis testing not an error free technique? In other words why can

Solution

a)In order to test the hypothesis for population mean the sample mean is needed to compute the test statistic which is against use to see whether the null hypothesis will be rejected or not. The confidence interval for mean is needed to compute because it gives that interval which contains the true population mean with say 95% confidence.

The standard error of mean is the sample standard deviation divided by root over the sample size.

The sampling distribution of mean approximately follows a normal distribution.

b)The hypothesis testing is not an error free technique, as sampling bias is always present there.

Type I error occurs when the null hypothesis rejected when it is actually true and type II error means when the null hypothesis is accepted when it is actually false. Both can never be zero due to sampling bias.

c) By a consistent estimator we mean if the sample size increases, the estimates usually converge to the true value of the parameter which is being estimated.

By an unbiased estimator we mean the true parameter value.