The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A ran

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The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A ran

dom sample of 25 rods has an average diameter of 0.5046 in.
a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume two-sided alternative and significance level of 0.05.
b) Find the p-value for test in part (a).
c) Construct a 95% two-sided confidence interval on the mean rod diameter.

Mathematics

1 answer:

lawyer [9.2K] · Answer 1 · 2026-03-14T13:22:13+03:00

a) The hypothesis states that the mean is different from 0.5025 and has been rejected. b) The p-value computed is 0. c) A confidence interval is established as 0.50456 < u < 0.50464. The hypothesis testing is based on a given standard deviation (s.d.) of 0.0001, a sample mean of x = 0.5046 from a sample size of n = 25. The two-sided alternative and significance level of 0.05 were assumed. A Z-score was calculated to show that the hypothesis is rejected since the mean differs from 0.5025.