# Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of

Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that $\mu <7$ hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of beta and interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)
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Step 1
Given info:
The power value is 0.4943 and population mean is 6.0 hours of sleep.
Step 2
Interpretation of Power of a hypothesis test:
The probability of rejecting the null hypothesis, when it is true. It is denoted by 1­-beta.
Power:$1-\beta =0.4943$
Thus, the power supports the claim that $\mu <7$ hours which is less compare to the real sleep time $\mu =6$ hours. If the power is 0.8 or high it is better.
beta value:
The probability of not rejecting null hypothesis when is false. It is denoted by beta.
$1-\beta =0.4943$
$\beta =1-0.4943$
$\beta =0.5057$
Interpretation of Type-II error:
Thus, the beta value is more than $50\mathrm{%}$ and it fails to support the claim $\mu <7$ hours. That is $\mu =6$ hours of sleep is necessary.