Suppose that 19 measurements of the failure stress of carbonfiber specimens results in a sample mean of 562.68 MPa and samplestandard deviation of 180.874 MPa and that the data is normallydistributed. Calculate two-sided confidence intervals for thefailure stress for the following cases:
a) 95% confidence interval for a single measurement (n = 1) ofthe failure stress. Assume that the population standard deviationis known to be 181 MPa.
b) 95% confidence interval for the sample mean with n = 19.Repeat for the 99% confidence interval. Assume that the populationstandard deviation is known to be 181 MPa
c) 95% confidence interval for the sample mean with n = 19.Repeat for the 99% confidence interval. Assume that the populationstandard deviation is UNKNOWN.
d) Suppose that an alternative process of producing carbonfibers results in a sample of failure stress measurements with n =12, sample mean = 650.32 MPa and sample standard deviation of130.470 MPa. What is the 95% confidence interval on the differencein failure stress between the two populations?
