本次美国代写是statistical quality control的一个assignment

Problem 1 (15 Pts)

Two different hardening processes, (1) saltwater quenching and (2) oil quenching, are used on
samples of a particular type of metal allow. The results are shown here. Assume that hardness is normally distributed.

a. Test the hypothesis that the mean hardness for the saltwater quenching process equals the
mean hardness for the oil quenching process. Use α=0.05 and assume equal variances.

b. Assuming that variances and 𝜎12 and 𝜎22 are equal, construct a 95% confidence interval
on the difference in mean hardness.

c. Construct a 95% confidence interval on the ratio𝜎12/𝜎22 . Does the assumption made
earlier of equal variance seem reasonable?

Problem 2 (10 Pt)

Consider the hypotheses 𝐻0: 𝜇 = 𝜇0 𝐻1: 𝜇 ≠ 𝜇0 where 𝜎2 is known. Derive a general
expression for determining the sample size for detecting a true mean of 𝜇1 ≠ 𝜇0 with probability
1 − 𝛽 if the type I error is α (Hint: the area of a very small left tail under the normal dist can be
assumed to be zero.)


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