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jameskarbar9p8c9d2
05.05.2020 •
Mathematics
For a hypothesis test of the claim that the mean amount of sleep for adults is less than 9 hours, technology output shows that the hypothesis test has power of 0.4038 of supporting the claim that muless than9 hours of sleep when the actual population mean is 8.5 hours of sleep. Interpret this value of the power, then identify the value of beta and interpret that value.
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Ответ:
a) probability of choosing the mean amount of sleep for adult as μ < 9 hours when it is μ = 8.5 hours is 0.4038
b) There is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is μ < 9 hours when it is μ = 8.5 hours
Step-by-step explanation:
a) Interpret the value of the power
The power of an hypothesis is the probability of rejecting the null hypothesis when the alternative hypothesis is valid. It is a type 1 error
Power = 0.4038
From the hypothesis test,
the null hypothesis, μ = 8.5 hours
Alternative hypothesis, μ < 9 hours
Sine the power is the probability of rejecting the null hypothesis, it means that the probability of choosing the mean amount of sleep for adult as μ < 9 hours when it is μ = 8.5 hours is 0.4038
b)
Power + β = 1
β = 1 - Power
β = 1 - 0.4038
β = 0.5962
β, type 2 error, is the probability of not rejecting the null hypothesis even when it is false.
It means that there is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is μ < 9 hours when it is μ = 8.5 hours
Ответ: