Question

An engineer who is studying the tensile strength of a steel alloy knows that tensile strength is approximately normally distributed with sigma= 60 psi. A random sample of 12 specimens has a mean tensile strength of 3450 psi.

a) Compute a two-side confidence interval on the maen tensile strength at a 95% confidence level.

b) Test the hypothesis that the mean strength is 3500 psi at alfa=0.05, and provide a conclusion statement.

c) If we keep the signifiance level constant (alpha). What would you recommend to make the interval smaller?

d) How would the interval change if we did not know that alpha=60 psi, but the number of specimens is 80?

e) How would the interval change if we did not know that sigma=60 psi, but the number of specimens is 10?

f) Explain if your answer in a) and b) agree with each other.

Answer 1

the first part of the solution for (a).

the final part of the solution for (a).

the solution for (b).

the solution for (c).

the first part of the solution for (d).

the final part for the solution for (d).

the solution for (e).

the solution for (f).