Despite its widespread usage in applications, null hypothesis testing has been critiqued for several reasons. For this paper, address the following prompts… 1) One of the critiques of null hypothesis testing is that, in reality, the null hypothesis is rarely, if ever, literally true. For example, you would rarely (if ever) expect the population mean to be, say, exactly 25 (as might be tested in a 2-tailed test). First, a) give a concrete example of carrying out a hypothesis test that demonstrates this critique and b) say why/how the critique applies in this example. Then, c) describe some additional statistical analysis/procedure that could be used (in general) to supplement a hypothesis test to (at least partially) address the critique and d) say why this would address the critique. 2) Another critique of null hypothesis testing is that, with very large samples, practically any test will be statistically significant. This implies that if you want a significant results, you just need to increase your sample size as large as possible. First, a) briefly describe why this is the case. Then, b) give a concrete example of carrying out a hypothesis test that demonstrates this critique and c) say why/how the critique applies in this example. Finally, Then, d) describe some additional statistical analysis/procedure that could be used (in general) to supplement a hypothesis test to (at least partially) address the critique and e) say why this would address the critique. Evaluation: You may address the questions within one continuous response or separately, but together the responses should be roughly 1 page, double-spaced. More important than the length is (1) whether you answered the all the questions directly and (2) whether you correctly use and interpret the ideas of (in this case) null hypothesis testing, confidence intervals, effect size, and power (implicitly or explicitly) in your responses. In general, try to be as concrete, specific, and explicit as possible, and don’t answer generically or by appealing only to definitions. Also, try to be concise and to directly address the questions. You do not need to include references, and you may use hypothetical examples.
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