Question

The desired percentage 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 using a significance level of .01, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = 0.3 and that ¯x = 5.25.

a. Does this indicate conclusively that the true average percentage differs from 5.5?

b. If the true average percentage is µ = 5.6 and a level α = .01 based on n = 16 is used, what is the probability of detecting this departure from H0?

 

c. What value of n is required to satisfy α = .01 and β(5.6) = .01?

Answer 1

Solution

a ) The null and alternative hypotheses can be defined as follows :

Ho : μ = 5.5 Vs H₂ : μ # 5.5

Under the null hypotheses the test statistics can be defined as follows :

Determine the P - value using excel function is shown below :

P - value : Using excel function the P - value is ,

P - value = 2Normsdist ( -3.13 ) = 0.002

Since , the P - value is less than the level of the significance . So , reject the null hypotheses .

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