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 ơ=0.32 and that x̅=5.21. (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 

Calculate the test statistic and determine the P-value.

State the conclusion in the problem context.

 Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage

 Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage

 Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage 

 Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.

 (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 H07(Round your answer to four decimal places.)

 (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.) 

Answer 1

a)

null hypothesis:Ho		μ	=	5.5
Alternate Hypothesis:Ha		μ	≠	5.5

test statistic           z             =

(x̄-μ)/σx=

-3.63

p value =0.0002 (try 0.0003 if this comes wrong)

reject the null; there is sufficient,,,,,,,,,

b)

probability =0.0919

c)

n =247