(c) (5 points) Suppose a sample of 81 measurements is seseeued l data set. If it
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(c) (5 points) Suppose a sample of 81 measurements is seseeued l data set. If it is possible, compute the probability that the average value of the 81 measurements is at between 22.85 dPa s and 22.95 dPa s. If it is not possible to compute, then say so. (10 points) Consider an experiment in which one measures radii of ball bearings (in cm.). The average radius of the ball bearings is unknown. However, the standard deviation of the radii measurements is 70 cm. (a) (5 points) A sample of 25 measurements has an average of 185 cm. If it is possible, find the 90 % confidence interval for the true average ra- dius of the data set. If it is not possible to find the interval, then say so. (b) (5 points) A sample of 49 measurements has an average of 185 cm. as well. If it is possible, find the 95 % confidence interval for the true average radius of the data set. If it is not possible to find the interval, then say so. 5 points) Consider an arbitrary data set with an arbitrary probability dis- ibution for the measurements. Then consider samples of size N and their mple averages. According to the central limit thooExplanation / Answer
Solution:- Given sd = 70 cm
a) n = 25 , mean = 185 , Z(0.05) = 1.645
90% conifdence interval for the true average radius of the data set:
=> X +/- Z*s/sqrt(n)
= 185 +/- 1.645*70/sqrt(25)
= (161.97 , 208.03)
b) n = 49 , mean = 185 , Z(0.025) = 1.96
95% conifdence interval for the true average radius of the data set:
=> X +/- Z*s/sqrt(n)
= 185 +/- 1.96*70/sqrt(49)
= (165.4 , 204.6)
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