Question

5. Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 3 lb. The standard weight of a container is 50 lbs. You are concerned that it may be as high as 50.6 lbs., however. If you test using a sample size of n 10, what is the probability of accepting the null hypothesis Ho' 50 when the weight is actually 50.6 lbs. ( .-0.05)? Assume weight is normally distributed.

Answer 1

Probability of accepting null hypothesis $H_0: \mu = 50 lb$ is equal to 1 minus P-value.

So first we need to calculate P-value.

P-value = P( Z > $\mid Z_{test value} \mid$ )​​​​​ = P( Z > $\mid 0.6325 \mid$ ) =2*P( Z < -0.6352) = 2*0.26355 = 0.5271

Where

$Z_{test value}$ = $\frac{\sqrt{n}(mean - \mu)}{\sigma}$ = $\frac{\sqrt{10}(50.6 - 50)}{3}$ = 0.6325

Probability of accepting null hypothesis = 1 - 0.5271 = 0.4729