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 ? = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of ?.

(a) Assuming this to be the case, if a sample of 49 modified bars resulted in a sample average yield point of 8465 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.) , lb

(b) How would you modify the interval in part (a) to obtain a confidence level of 92%? (Round your answer to two decimal places.) should be changed to .

Answer 1

Since the population standard deviation is given, so we will use the z statistic

we have = 100, =8465 and sample size = 49

(A) we know that the z critical for 90% confidence interval is 1.645 using the normal distribution table

Using the confidence interval formula, we can write it as  

CI =

setting the given values, we get

CI =

So, the 90% confidence interval is (8441.5, 8488.5)

(B) Only the value of critical z score will get changed on changing the confidence interval level

Using the normal distribution table, the z critical value corresponding to 92% confidence level is given as z score = 1.75

so, setting the value of z score in the confidence interval equation, we get

CI =

setting the given values, we get

CI =

So,the required 92% confidence interval is (8440.00, 8490.00)