For a hypothesis test of the claim that the mean amount of sleep for adults is less than 8 hours, technology output shows that the hypothesis test has power of 0.4009 of supporting the claim that muless than8 hours of sleep when the actual population mean is 7.0 hours of sleep. Interpret this value of the power, then identify the value of beta and interpret that value.

Interpret this value of the power.

Step-by-step explanation:

The power of a test or the statistical power is defined as the probability that it will reject the null hypothesis when it is false. It is also is the probability of avoiding a Type II error (beta). The statistical power is affected mainly by four things:

Significance level (or alpha)

Sample size

Variability

Magnitude of the effect of the variable.

In this study, the technology output shows that the hypothesis test has power of 0.4009. This means that there is a 41% chance of ending up with a p value of less than 5% in this test.

Mathematically, power is 1 - beta

Which is 1 - 0.4009 = 0.5991. But the beta is commonly set at 0.2, leaving us with a standard power of 0.8

In this study, we have a beta value of 0.5991, which is a lot higher than the standard 0.2, thus we run the high risk of making a type II error (failing to reject the null hypothesis when false).

We can conclude that this power is inadequate or excessive risk of type II error making drawing a conclusion using this test not statistically possible.