Question

For a hypothesis test of the claim that the mean amount of sleep for adults is less than 6 ​hours, technology output shows that the hypothesis test has power of 0.4272 of supporting the claim that μ<6 hours of sleep when the actual population mean is 4.0 hours of sleep. Interpret this value of the​ power, then identify the value of β and interpret that value.

Answer 1

Answer:

#$\beta=0.5492$

#This Value of $\beta$ goes to indicate that there is greater $50\%$ probability that $\mu<8$ will not be acknowledged at $\mu =5$

Step-by-step explanation:

From the question we are told that:

Amount of sleep for adults $X=P(< 6)$

Hypothesis test has power $p=0.4272$

Mean $\=x =4hours$

Generally the equation for $\beta$ is mathematically given by

$\beta=1-P$

$\beta=1-0.4508$

$\beta=0.5492$

Therefore

This Value of $\beta$ goes to indicate that there is greater $50\%$ probability that $\mu<8$ will not be acknowledged at $\mu =5$