Answer Happy

The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o - 0.32 and that x = 5.22. (Use it = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: A = 5.5 = 5.5 OH, u = 5.5 H:>> 5.5 OH : 4 = 5.5 H.: 5.5 O Ho: 4 = 5.5 HU<5.5 four decimal places.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value Z= P-value = State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is x = 5.6 and a level a = 0.01 test based on 11 = 16 is used, what is the probability of detecting this departure from H,? (Round your answer to four decimal places.)

= (C) What value of n is required to satisfy a = 0.01 and B(5.6) = 0.01? (Round your answer up to the next whole number.) samples n =