In order to test the quality of a certain brand of rivets, an engineer randomly

Question

In order to test the quality of a certain brand of rivets, an engineer randomly selects n = 50 rivets from a large
batch and measures their breaking strength. The sample mean breaking strength of the sampled rivets was
9,720 psi and the sample standard deviation was 485.
(a) Calculate the standard error of the mean.
(b) Calculate an approximate 95% confidence interval for the true mean breaking strength.
(c) One of the claims made by the company producing the rivets is that the true mean breaking strength is
10,000 psi. Does the engineer have evidence that this claim is likely to be false? Explain.

Explanation / Answer

Answer to the questions below:

a. Standard error = Stdev/sqrt(n) = 485/sqrt(50) = 68.59

b. 95% CI is given by : Xbar +/- Z*SE = 9720 +/- 1.96*68.59 = 9585.564 to 9854.436

c.One of the claims made by the company producing the rivets is that the true mean breaking strength is
10,000 psi. It is FALSE as the 95% confidence interval doesn't have the 10000 psi in its range. Hence, the claim is most likely to be FALSE

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