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Identify the rejection region(s). Select the correct choice below.
A. The rejection regions are z < -2.33 and z > 2.33.
B. The rejection region is z > 2.33.
C. The rejection region is z < 2.33.

Identify the rejection region(s). Select the correct choice below.\newlineA. The rejection regions are z<-2.33 and z>2.33 .\newlineB. The rejection region is z>2.33 .\newlineC. The rejection region is z<2.33 .

Full solution

Q. Identify the rejection region(s). Select the correct choice below.\newlineA. The rejection regions are z<2.33 z<-2.33 and z>2.33 z>2.33 .\newlineB. The rejection region is z>2.33 z>2.33 .\newlineC. The rejection region is z<2.33 z<2.33 .
  1. Understand the context: Understand the context of the rejection region.\newlineThe rejection region(s) in a hypothesis test are the range(s) of values for which the null hypothesis is rejected. These regions are determined based on the significance level (α\alpha) and the type of test (one-tailed or two-tailed).
  2. Determine test type: Determine the type of test based on the given options.\newlineOptions A and B suggest a two-tailed test because they mention both tails of the distribution. Option C suggests a one-tailed test because it mentions only one tail of the distribution.
  3. Identify rejection region: Identify the correct rejection region(s) based on the z-values provided. The z-values given are 2.33-2.33 and 2.332.33. These are likely related to a specific significance level in a standard normal distribution. For a two-tailed test, the rejection regions would be both tails beyond these z-values. For a one-tailed test, the rejection region would be only one tail beyond the z-value.
  4. Match z-values: Match the z-values to a significance level.\newlineTypically, z-values like 2.332.33 correspond to a specific significance level. For example, a z-value of approximately 2.332.33 corresponds to a significance level of 0.010.01 in a two-tailed test (0.0050.005 in each tail). This means that option A is likely correct if the significance level is 0.010.01 for a two-tailed test.
  5. Confirm test type: Confirm the type of test and the significance level. Without additional information about the significance level or the type of test (one-tailed or two-tailed), we cannot definitively choose between options A, B, and C. However, based on common practice and the symmetry of the zz-values provided, we can infer that a two-tailed test is likely, making option A the correct choice.
  6. Find test statistic: Find the standardized test statistic.\newlineTo find the standardized test statistic, we would typically use a formula or technology as indicated in the problem. However, without specific data or a test statistic provided, we cannot calculate this value. The problem asks us to use technology, which suggests that we would input data into a statistical software or calculator to obtain the test statistic.

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