A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more

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A mixture of pulverized fuel ash and Portland cement to be used
for grouting should have a compressive strength of more than 1,300
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 = 59. Let 𝜇 denote the true
average compressive strength.
(a)
What are the appropriate null and alternative hypotheses?
H0: 𝜇 > 1,300
Ha: 𝜇 =
1,300H0: 𝜇 = 1,300
Ha: 𝜇 >
1,300 H0: 𝜇 <
1,300
Ha: 𝜇 =
1,300H0: 𝜇 = 1,300
Ha: 𝜇 <
1,300H0: 𝜇 = 1,300
Ha: 𝜇 ≠ 1,300
(b)
Let
X
denote the sample average compressive strength
for n = 11 randomly selected
specimens. Consider the test procedure with test
statistic
X
itself (not standardized). What is the probability
distribution of the test statistic
when H0 is true?
The test statistic has a binomial distribution.The test
statistic has a gamma distribution. The test
statistic has an exponential distribution.The test statistic has a
normal distribution.
If
X = 1,340,
find the P-value. (Round your answer to four
decimal places.)
P-value =
Should H0 be rejected using a
significance level of 0.01?
reject H0do not
reject H0
(c)
What is the probability distribution of the test statistic
when 𝜇 = 1,350 and n = 11?
The test statistic has a gamma distribution.The test statistic
has a binomial distribution. The test
statistic has an exponential distribution.The test statistic has a
normal distribution.
State the mean and standard deviation (in KN/m2) of
the test statistic. (Round your standard deviation to three decimal
places.)
mean KN/m2standard
deviation KN/m2
For a test with 𝛼 = 0.01, what is the probability that
the mixture will be judged unsatisfactory when in
fact 𝜇 = 1,350 (a type II error)? (Round your answer
to four decimal places.)