A journal article reports that a sample of size 5 with a sample mean of 231.634 and a sample variance of 2.268 was used as a basis for calculating two confidence intervals for the true average natural frequency (Hz) of delaminated beams of a certain type. Both intervals were calculated from the same sample data. The resulting intervals were (230.2, 233.07) and (229.11, 234.16).
(a) Determine the confidence levels of the two intervals.
(b) You decide that a confidence level of 97.5% is more appropriate than the levels used. What are the limits of the 97.5% interval?