Identify the rejection region(s). Select the correct choice below. $\newline$ A. The rejection regions are $z<-2.33$ and $z>2.33$ . $\newline$ B. The rejection region is $z>2.33$ . $\newline$ C. The rejection region is $z<2.33$ . $\newline$ (c) Find the standardized test statistic. Use technology.

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Algebra 1

Write and solve direct variation equations

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Q. Identify the rejection region(s). Select the correct choice below.

\newline

A. The rejection regions are

z<-2.33

and

z>2.33

\newline

B. The rejection region is

z>2.33

\newline

C. The rejection region is

z<2.33

\newline

Understand the context: Understand the context of the rejection region. $\newline$ The 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 ( $\alpha$ ) and the type of test (one-tailed or two-tailed).
Determine test type: Determine the type of test based on the given options. $\newline$ Options 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.
Identify rejection region: Identify the correct rejection region(s) based on the z-values provided. The z-values given are $-2.33$ and $2.33$ . 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.
Match z-values: Match the z-values to a significance level. $\newline$ Typically, z-values like $2.33$ correspond to a specific significance level. For example, a z-value of approximately $2.33$ corresponds to a significance level of $0.01$ in a two-tailed test ( $0.005$ in each tail). This means that option A is likely correct if the significance level is $0.01$ for a two-tailed test.
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 $z$ -values provided, we can infer that a two-tailed test is likely, making option A the correct choice.
Find test statistic: Find the standardized test statistic. $\newline$ To 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.