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-70. Let μ denote the true average compressive strength. a) What are the a null and altenative hypotheses? Ho: 1300 на: #1300 Ho:> 1300 hja: μ-1300 H0: μ 1300 Hai H 1300 НО: #1300 1300 #1300 -1300 НО: на: (b) Let X denote the sample average compressive strength for n-15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? The test statistic has a gamma distribution. o The test statistic has a binomial distribution. o The test statistic has an exponential distribution. a The test statistic has a normal distribution fX- 1340, find the P-value. (Round your answer to four decimal places.) P-value- Should Ho be rejected using a significance level of 0.01? o reject Ho e do not reject Ho c) What is the The test statistic has a binomial distribution. s The test statistic has a normal distribution. o The test statistic has an exponential distribution. o The test statistic has a gamma distribution. ability distribution of the test statistic when1350? State the mean and standard deviation of the test statistic. (Round your standard deviation to three decimal places.) KN/m standard deviation KN/m2 For a test with a 0.01, what is the probability that the mixture will be judged u when in fact μ-1350 (a type II error)? (Round your answer to four decimal places.)

Answer 1

P-Value: 0.0133

mean = 1340

Standard deviation = 65/sqrt(13) = 18.0278