On the basis of extensive tests, the yield point of a particular type of mild st

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 sigma = 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 sigma. (a) Assuming this to be the case, if a sample of 16 modified bars resulted in a sample average yield point of 8496 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.) (b) How would you modify the interval in part (a) to obtain a confidence level of 96%? The value of z should be changed to You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

PART A.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=8496
Standard deviation( sd )=100
Sample Size(n)=16
Confidence Interval = [ 8496 ± Z a/2 ( 100/ Sqrt ( 16) ) ]
= [ 8496 - 1.64 * (25) , 8496 + 1.64 * (25) ]
= [ 8455,8537 ]

b.
Z value be modified to 2.05

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