Confidence intervals and hypothesis tests.

A random variable is assumed to follow a normal distribution with population variance equal to 10^2. Calculate a 95% confidence interval for the mean if you take a random sample of 20 observations and find the sample mean is equal to 50.

For the confidence interval in part (a), is the population mean is different from 53? Why or why not?

Assume that you have a random sample of 20 observations where the sample mean is equal to 50 and the sample variance is 81. Do you have enough evidence to conclude that the population mean is different from 46 at a 5% level of significance?