A mixture of pulverized fuel ash and Portland cement to be usedfor grouting should have a compressive strength of more than 1300KN/m². The mixture will not be used unless experimentalevidence indicates conclusively that the strength specification hasbeen met. Suppose compressive strength for specimens of thismixture is normally distributed with ? = 66. Let? denote the true average compressive strength.

(a) What are the appropriate null and alternativehypotheses?

H₀: ? = 1300
H_a: ? > 1300H₀:? > 1300
H_a: ? =1300    H₀: ? =1300
H_a: ? ? 1300H₀:? < 1300
H_a: ? = 1300H₀:? = 1300
H_a: ? < 1300

(b) Let

X

denote the sample average compressive strength for n =14 randomly selected specimens. Consider the test procedure withtest statistic

X

itself (not standardized). What is the probability distributionof the test statistic when H₀ is true?

The test statistic has a gamma distribution.The test statistichas a normal distribution.    The teststatistic has a binomial distribution.The test statistic has anexponential distribution.

If

X = 1340,

find the P-value. (Round your answer to four decimalplaces.)
P-value =

Should H₀ be rejected using a significancelevel of 0.01?

reject H₀do not rejectH₀   

(c) What is the probability distribution of the test statistic when? = 1350?

The test statistic has an exponential distribution.The teststatistic has a normal distribution.    Thetest statistic has a gamma distribution.The test statistic has abinomial distribution.

State the mean and standard deviation of the test statistic. (Roundyour standard deviation to three decimal places.)

mean		KN/m2
standard deviation		KN/m2

For a test with ? = 0.01, what is the probability that themixture will be judged unsatisfactory when in fact ? =1350 (a type II error)? (Round your answer to four decimalplaces.)