1. Determine what would happen to your critical value (Z) if you were to change the level of significance (a) from .05 to .1 in a two tailed hypothesis test.
2. Why would the critical value change in the way you predict?
3. What does this suggest about the trade offs between Type 1 and Type II errors?
Please give some examples so I understand the concepts. Thank you.
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1. Determine what would happen to your critical value (Z) if you were to change the level of significance (a) from .05 to .1 (.01?) in a two-tailed hypothesis test.
In hypothesis testing, the significance level is the criterion used for rejecting the null hypothesis. The significance level is used in hypothesis testing as follows: First, the difference between the results of the experiment and the null hypothesis is determined. Then, assuming the null hypothesis is true, the probability of a difference that large or larger is computed. Finally, this computed probability is compared to the significance level (.05 or .01, etc.).
If the probability is less than or equal to the significance level (critical value of Z), then the null hypothesis is rejected and the outcome is said to be statistically significant. Traditionally, experimenters have used either the .05 level (sometimes called the 5% level) or the .01 level (1% level), although the choice of levels is largely subjective. The lower the significance level, the more the data must diverge from the null hypothesis to be significant. Therefore, the .01 level is more conservative than the .05 level. The Greek letter alpha is sometimes used to indicate the significance level. (http://davidmlane.com/hyperstat/A72117.html),
The corresponding critical value of z is pre-computed for us in a z-score chart, which corresponds to the alpha level and the type of test (one or two tailed). For example, .05 two-tailed test has a pre-calculated corresponding critical value of z and .01 has another, which you look up on the chart. As the significance level decreases (from .05 to .01), the critical value of Z increases. In other words, the lower the significance level, the more the data must diverge from the null hypothesis to be significant.
2. Why would the critical value change ...
By responding to the questions and with examples, this solution addresses aspects of research, statistics and evaluation.