Instructions Show all relevant workings . Use the normal distribution curve to illustrate your answer The following simple random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3, 1. Construct a 90% confidence interval for the population mean u. 2. Construct a 95% confidence interval for the population mean u. 3. Construct a 99% confidence interval for the population mean u. 4. Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that they are based on a sample of n = 25 observations rather than n = 6 observations. Repeat parts 1-3. What is the effect of increasing the sample size on the width of the confidence intervals? Select True or False for questions 5 and 6 5. The 95 % confidence interval will be wider than a 90% confidence interval 6. In constructing a confidence interval for the population mean, the t distribution should never be used whenever n > 30