Question

What is the form of a confidence interval? That is, what goes where?

34 If we calculate a 95% confidence interval, what is the risk that we have made a mistake?

35 Say we have a 95% confidence interval that goes from 4.0 to 6.0. Describe the mistake from question 34, fully.

Answer 1

Solution:

The 95% confidence for population mean is given as follows:

where, xbar is sample mean, sigma is population standard deviation, n is sample size. Z_(0.05/2) is critical z-value for 95% confidence interval.

95% confidence interval for population mean can be interpreted as follows:

We are 95% confident that true value of population mean lies within the calcuted confidence limits (both values are inclusive).

34) If we calculate a 95% confidence interval then we are 95% confident that the true value of the parameter lies within the calculated confidence limits. But remaining 5% confidence is doubtful. So this 5% lack of confidence is the risk that we have made a mistake.

35) Our calculated 95% confidence interval is (4, 6). It means we are 95% confident that the true value of the parameter lies within 4 and 6 (both values are inclusive). But due to lack of 5% confidence level it may that true value of population parameter falls outside the confidence limits. So this lack of 5% confidence level can be a cause of mistake that we can do.

Note: When we increase the confidence level to calculate confidence interval, chance of doing mistake reduces.