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 ? = 0.26 and that x = 5.25.

(a) Find the test statistic

(b) If the true average percentage is ? = 5.6 and a level ? = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H₀? (Give answer accurate to 3 decimal places.)

(c) What value of n is required to satisfy ? = 0.01 and ? (5.6) = 0.01? (Exact answer required.)

Answer 1

a)test statistic =(5.25-5.5)*sqrt(16)/0.26 =-3.85

p value =0.0002

b)

probability of detecting this departure from H₀ =0.149

c)

n=163