6. A diamond-cutting machine has been set to turn out diamonds of “0.5-karat” weight.

Assume from past experience that the machine produces diamonds of weight that 432 9 Hypothesis Testing has the N(μ, 0.0036) distribution. It is important to a jewelry supply house that the weight not be too low (dissatisfied customers) or too high (economic considerations).

Accordingly, the machine is checked every so often. A recent sample of six diamonds yielded weights of 0.48, 0.59, 0.54, 0.50, 0.55, and 0.56 karats. Test at the 5% level of significance the hypothesis H0: μ = 0.5 versus H1: μ = 0.5