Question

On the basis of extensive tests, the yield point of a particular type of mild steel reinforcing bar is known to be normally distributed with a standard deviation of 415 Nt. The composition of the bar has been slightly modified, but the modification is not believed to have affected the normality or the standard deviation.
Assuming this to be the case, if a sample of 24 modified bars resulted in a sample average yield point of 32490 Nt, construct a 95% confidence interval for the true average yield point of the modified bar.

zα	1.282	1.645	1.960	2.326	2.576	3.090
α(tail area)	0.1	0.05	0.025	0.01	0.005	0.001
%ile	90	95	97.5	99	99.5	99.9

Your answers can be rounded to one decimal digit accuracy when entered.

Lower limit is =				Upper limit is =

Answer 1

Given that, population standard deviation = 415 Nt

sample size ( n ) = 24

sample mean = 32490 Nt

A 95% confidence level has significance level of 0.05 with tail area is 0.025 and critical value is,

The 90% confidence interval for the true average yield point of the modified bar is,

Where, Lower limit = 32324.0 and Upper limit = 32656.0