A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?Group of answer choicesA sample mean much different than 80 with α = .05A sample mean near 80 with α = .05A sample mean near 80 with α = .01A sample mean much different than 80 with α = .01
Question
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?Group of answer choicesA sample mean much different than 80 with α = .05A sample mean near 80 with α = .05A sample mean near 80 with α = .01A sample mean much different than 80 with α = .01
Solution
A sample mean much different than 80 with α = .01.
Here's why:
The null hypothesis in this case would likely be that the treatment has no effect, meaning the sample mean would be equal to the population mean (80).
To reject the null hypothesis, we need strong evidence that the treatment does have an effect, which would be indicated by a sample mean that is significantly different from the population mean.
The alpha level (α) is the probability of rejecting the null hypothesis when it is true (a type I error). A lower alpha level means you require stronger evidence to reject the null hypothesis.
Therefore, a sample mean much different than 80 with a low alpha level (α = .01) would provide the strongest evidence against the null hypothesis, making it the most likely to result in rejecting the null hypothesis.
Similar Questions
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