SOLVE BOLDED GIVE EXACT ANSWER A mixture of pulverized fuel

SOLVE BOLDED. GIVE EXACT ANSWER.

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 = 59. Let 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 = 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?

If

X = 1340,

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

Should H₀ be rejected using a significance level of 0.01?

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

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

mean= _______________KN/m2

standard deviation=_____________ KN/m2

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

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

a)

H0: = 1300
Ha: > 1300

1340 - 1300 / 59

Z = 0.68

P value : 0.2483

do not reject Ho

The test statistic has a normal distribution