An electric sale gives a reading equal to the true weight plus a random error that isnormally distributed with mean 0 and standard deviationσ=.1 mg. suppose that the results of fivesuccessive weightings of the same object are as follows: 3.142, 3.163, 3.155, 3.150, 3.141.(a) determine a 95 percent confidence interval estimate of the true weight.
(b) determine a 99 percent confidence interval estimate of the true weight.

a) 95% confidence interval estimate of the true weight is (3.026, 3.274)

b) 99% confidence interval estimate of the true weight is (2.944, 3.356)

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

M is the mean of five successive weightings (3.150)ME is the margin of error from the mean

And margin of error (ME) can be calculated using the formula

ME= where

t is the corresponding statistic in the given confidence level and degrees of freedom(t-score) s is the standard deviation of the random error (0.1)N is the sample size (5)

Using the numbers 95% confidence interval estimate of the true weight is:

3.150±≈3.150±0.124

And 99% confidence interval estimate of the true weight is:

3.150±≈3.150±0.206

The answer is

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