What are the two rejection areas in using a two-tailed test and the 0.01 level of significance?
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A. B. C. D. E.E
0.01 means that we are considering a 99% level of significance. For this, we can find the z-value to be +/- 2.58.
In hypothesis testing, a two-tailed test is used when we are interested in determining whether there is a significant difference between two groups, but we do not have a specific direction in mind. The 0.01 level of significance (also known as alpha level) indicates the maximum probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.
To identify the rejection areas in a two-tailed test with a significance level of 0.01, we need to find the critical values that divide the sampling distribution into two tails, each representing 0.01 of the area under the curve.
The critical values are determined by the chosen significance level and the distribution of the test statistic. The most commonly used distribution for hypothesis testing is the standard normal distribution (also known as the Z-distribution) when dealing with large sample sizes. In this case, the critical values can be found using the Z-table or a statistical calculator.
For a two-tailed test with a 0.01 level of significance, we need to split the significance level equally between the two tails. Since the standard normal distribution is symmetric, we allocate 0.005 to each tail.
To find the critical values, we need to locate the Z-scores that correspond to an area of 0.005 in each tail. In the standard normal distribution, the Z-score represents the number of standard deviations a data point is from the mean. We can find these Z-scores by looking up the values in the Z-table or using a statistical calculator.
Looking up the Z-table, we find that the critical Z-score for a one-tailed test with a 0.005 area in the upper tail is approximately 2.58. Similarly, the critical Z-score for a 0.005 area in the lower tail is approximately -2.58.
Therefore, the correct answer is E. Above 2.58 and below -2.58. These values represent the two rejection areas for a two-tailed test with a 0.01 level of significance when using the standard normal distribution. Any test statistic falling outside these rejection areas would lead to rejecting the null hypothesis in favor of the alternative hypothesis.