Question

The desired percentage of SiO2 in aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a certain production facility, n = 16 independently obtained samples were analyzed and it was found that ¯x = 5.25. Suppose that the percentage of Si O2 found in the sample is normally distributed with σ = 0.3 and. (a) Does this indicate that the true average percentage differs from 5.5? Use significance level α = 0.01 (b) Repeat the calculation in the case where σ is unknown and s = 0.3

Answer 1

a)

H0: = 5.5

Ha: 5.5

Test statistics

z = - / / sqrt(n)

= 5.25 - 5.5 / 0.3 / sqrt(16)

= -3.33

Critical value at 0.01 level = -2.576 , 2.576

Since test statistics falls in rejection region, reject the null hypothesis.

b )

Test statistics

z = - / S / sqrt(n)

= 5.25 - 5.5 / 0.3 / sqrt(16)

= -3.33

t critical value at 0.01 level with 15 df = -2.947 , 2.947

Since test statistics falls in rejection region, reject the hull hypothesis.