You want to investigate a claim about the average loudness of certain vacuum cleaners. Suppose the sound intensity is a path that has a standard normal distribution of 3.6 dB. Specifically, Ho: Mu = 75.20 was tested against H1: Mu> 75.20 Based on measurements of the sound intensity of n = 15 of such machines with alpha = 0.05 The probability of a type II error was then calculated for Mu = 77 dB (Image 1) Now: Calculate the power Mu1 = 77 when: a) The level changes to alpha = 0.03 b) alpha = 0.05 but the alternative changes to two-sided H1: Mu different from 75.2
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
You want to investigate a claim about the average loudness of certain vacuum cleaners. Suppose the sound intensity is a path that has a standard
Specifically, Ho: Mu = 75.20 was tested against H1: Mu> 75.20
Based on measurements of the sound intensity of n = 15 of such machines with alpha = 0.05
The
(Image 1)
Now:
Calculate the power Mu1 = 77 when:
a) The level changes to alpha = 0.03
b) alpha = 0.05 but the alternative changes to two-sided
H1: Mu different from 75.2
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