Referring to Exercise 7.82 and using 14,380 as an estimate of \(\sigma\), find the sample size that would have been needed to be able to assert with \(95 \%\) confidence that the sample mean is off by at most 10,000. First estimate \(n_{1}\) by using \(z=1.96\), then use \(t_{0.025}\) for \(n_{1}-1\) degrees of freedom to obtain a second estimate \(n_{2}\), and repeat this procedure until the last two values of \(n\) thus obtained are equal.]

Data From Exercise 7.82 

Transcribed Image Text:

7.82 In order to test the durability of a new paint, a high- way department had test strips painted across heavily traveled roads in 15 different locations. If on the av- erage the test strips disappeared after they had been crossed by 146,692 cars with standard deviation of 14,380 cars, construct a 99% confidence interval for the true average number of cars it takes to wear off the paint. Assume a normal population.