Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviati
on of three points. A random sample of 36 scores is taken and gives a sample mean of 68. Find a 85 % confidence interval estimate for the population mean exam score. Explain what the confidence interval means
Let mu be the true population mean of statistics exam scores. We have a large random samples of n=36 scores with a sample mean of 68.we know that the population standard deviation is sigma=3.A pivotal quantity is 3^sqrt(36)=(3/6)=68(1/2) which is approximately normally distributed. Therefore the 85%confidence interval is 68-(1/2)(1.6449), 68+(1/2)(1.6449) i.e (67.18,68.82)
