MINITAB calculation of power These calculations pertain to normal populations with known variance and provide an accurate approximation in the large sample case where \(\sigma\) is unknown. To calculate the power of the \(Z\) test at \(\mu_{1}\), you need to enter the

\[\text { difference }=\mu_{1}-\mu_{0}\]

Although \(n=15\) is not large, we illustrate with reference to the example concerning average sound intensity on page 260 , where \(\alpha=0.05, \sigma=3.6\), and \(H_{1}: \mu>75.2\). We are given \(\mu_{1}=77\), so the difference \(=\mu_{1}-\mu_{0}=77-75.2=1.80\).

Referring to the example of machine parts on page 260 .

(a) Calculate the power at \(\mu_{1}=2.020\).

(b) Repeat part

(a) but take \(\alpha=0.03\).

Output: (partial)

Transcribed Image Text:

Stat > Power and sample size > 1-Sample Z. Type 15 in Sample sizes, 1.8 in differences and 3.6 in Standard deviation. Click Options and choose Greater than. Type 0.05 in Significance level. Click OK. Click OK.