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 historical standard deviation 100. A sample of 35 bars was taken and has a sample mean of 8439 lbs. Suppose that the specications are that the yield point of a particular type of mild steel-reinforcing bar should be 8475 lbs. (a) In performing one-sample hypothesis tests, would we use z? or t? in this situation? Briey explain why you would use one instead of the other.

(b) Is there sucient evidence that the mean yield point is less than the specications call for (the specs say 8475)? Conduct a hypothesis test, using the pvalue approach

. (c) State the kind of error could have been made in context of the problem.

(d) Now do part b again in R

Explanation / Answer

a)

b)

Test hypothesis are

Null hypothesis

          Ho: 8475

Alternative hypothesis

          HA: < 8475

x=8439

z= (x-) / (/sqrt(n))

=(8439 -8475) /(100/sqrt(35))

= -2.1297

P(z<-2.1297) = 0.0166

hence the probability is 0.0166

p- value <0.05 , hence reject H0

c) .Type I error:- reject the null hypothesis

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