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Question

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ= 60. Let μ denote the true average compressive strength. a. What are the appropriate null and alternative hypotheses? b. Let X denote the sample average compressive strength for n = 10 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). If x =1340, should H0 be rejected using a significance level of .01? [Hint: What is the probability distribution of the test statistic when H0 is true?] c. What is the probability distribution of the test statistic when μ=1350? For a test with α = .01, what is the probability that the mixture will be judged unsatisfactory when in fact μ= 1350 (a type II error)?

          
            A mixture of pulverized fuel ash and Portland cement to be used
for grouting should have a compressive strength
of more than 1300 KN/m2. The mixture will
not be used unless experimental evidence indicates conclusively
that
the strength specification has been met. Suppose compressive
strength for specimens of this mixture is normally
distributed with σ= 60. Let μ denote the true average
compressive strength.
a. What are the appropriate null and
alternative hypotheses?
b. Let X denote
the sample average compressive strength for n = 10
randomly selected specimens. Consider the test procedure with test
statistic X itself
(not standardized). If x =1340, should
H0 be rejected using a significance level of
.01? [Hint: What is the probability distribution of the
test statistic when H0 is true?]
c. What is the probability distribution of the
test statistic when μ=1350? For a test with α =
.01, what is the probability that the mixture will be judged
unsatisfactory when in fact μ= 1350 (a type II error)?

Added by Robert W.

Instant Answer

Step 1

The appropriate null and alternative hypotheses are: H0: μ ≤ 1300 (The true average compressive strength is less than or equal to 1300 KN/m2) H1: μ > 1300 (The true average compressive strength is greater than 1300 KN/m2) b. To determine if H0 should be Show more…

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