Question

Please provide a step by step solution. The most confusing thing is that I don't know how to find t value of 97% confident interval on the T-table.

A shoe store wants to estimate the average shoe size of their customers. It is assumed that the shoe size of their customers follows a normal distribution. It is known from previous experience that the standard deviation of shoe size is 2.4 inches. They take a sample of 40 customers and obtains the average shoe size of 10.3 inches from them. Estimate a 97% confidence interval for the population mean. 10.3 +/-

Answer 1

Given that n=40, 1 =10.3,and o=2.4. The confidence level is given to be 0.97, therefore, significance level can be obtained as follows: a=1-0.97 = 0.03 The critical value Zap at 0.03 level of significance is 2.17 (from standard normal tables). Therefore, the 97% confidence interval is computed as follows: 5+Zgle =10.3 + (2.17) ZA = 10.3+0.8235 = (9.4765, 11.1235) Thus, the 97% confidence interval is (9.4765 , 11.1235))