Question

According to a sample of 200 various insurance brokers and health experts, a typical childbirth in the United States costs on average $9500 with a standard deviation of $2500. Use the sample data to construct a 95% confidence interval estimate of the population mean μ.

a. Calculate the sample mean.

b. Calculate the standard error.

c. Find the critical value.

d. Construct the confidence interval

Answer 1

a) sample mean = 9500

b) standard error = sd / sqrt(n) = 2500 / sqrt(200) = 176.78

c) Critical value = Z_0.025 = 1.96

d) Confidence interval = (sample mean + Z_0.025 * standard error)

                                    = (9500 + 1.96 * 176.78)

                                    = (9500 + 346.48)

                                    = (9153.52 , 9846.48)