Question

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.

Answer 1

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)

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=
`(t*s)/(√(N) )` 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±
`(2.776*0.1)/(√(5) )`≈3.150±0.124

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

3.150±
`(4.604*0.1)/(√(5) )`≈3.150±0.206