A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n = 9 participants is selected, and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with µ = 240 and σ = 30. Use the Distributions tool to answer the questions that follow. If the researcher uses a two-tailed test with α = .05, what is the power of the hypothesis test? The power for the test is the probability of obtaining a z-score than , which is p = . Again, assuming a two-tailed test with α = .05, what is the power of the hypothesis test if the sample size is increased to n = 25? The power for the test is the probability of obtaining a z-score than , which is p =
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!
A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n = 9 participants is selected, and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with µ = 240 and σ = 30. Use the Distributions tool to answer the questions that follow.
Given,
Population mean before treatment = 240
Population mean after treatment = 210
Standard deviation is 30.
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