Question

The desired percentage of SiO2 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 SiO2 in a sample is normally distributed with σ = 0.32 and that x = 5.23. (Use α = 0.05.)

(a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses.

: μ = 5.5 Ha: μ ≠ 5.5 Correct: Your answer is correct.

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z = -3.6 Incorrect: Your answer is incorrect.

P-value = 0.0003 Incorrect: Your answer is incorrect.

(b) If the true average percentage is μ = 5.6 and a level α = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0? (Round your answer to four decimal places.) 0.1071 Incorrect: Your answer is incorrect.

(c) What value of n is required to satisfy α = 0.01 and β(5.6) = 0.01? (Round your answer up to the next whole number.)

n = __________. samples

Answer 1

(a)

(b)

(c)