Consider an experiment in which one measures the radii of a ball bearings (in cm). The average radius of the ball is unknown. However, the standard deviation of the radii measurement is 70 cm.
a. A sample of 25 measurements has an average of 185 cm. If it is possible, find the 90 % confidence interval for the true average radius of the data set. If it is not possible to do so, then say so.
b. A sample of 49 measurements has an average of 185 cm as well. If it is possible, find the 90 % confidence interval for the true average radius of the data set. If it is not possible to find the interval, then say so.
c. With 90% confidence, compute the maximum error between the sample average of the 49 radii measurements of the previous problem and the true average radius of the data set.
d. With 90% confidence, compute the minimum sample size N, necessary to ensure that the error between the true average radius and the sample average radius of the N measurements is less than or equal to 10 cm. Assume again that the standard deviation of all the measurements is 70 cm.