Use α\alpha to find the critical value(s), then determine if the given test statistic is in the rejection region.(A)\left(A\right) H0:μ=7.5;Ha:μ>7.5H_0:μ=7.5; H_a:μ>7.5α=0.01;z=2.17α=0.01; z=2.17Test is [ LEFT | TWO | RIGHT ] -tailedCritical Value(s):Test stat [ IN | NOT IN ] rejection region.

Test is RIGHT -tailed, Critical value(s): 2.33 2.33 2.33 , Test stat NOT IN rejection region.

Use α \alpha to find the critical value(s), then determine if the given test statistic is in the rejection region. ( A ) \left(A\right) H 0 : μ = 7.5 ; H a : μ > 7.5 H_0:μ=7.5; H_a:μ>7.5 α = 0.01 ; z = 2.17 α=0.01; z=2.17 Test is [ LEFT | TWO | RIGHT ] -tailed Critical Value(s): Test stat [ IN | NOT IN ] rejection region.

Welcome back. In this problem, we'd like to use alpha to find the critical value or values and then determine if the given test statistic is in the rejection region. For part a, we've been given our hypotheses, we've been given alpha, and we've been given the test statistic, which is a z score of 2.17. So the first thing we need to do is determine if our hypothesis test is left tailed, two tailed, or right tailed. That's gonna help us determine if we have one or two critical values, and also how to get our critical value. Looking at our alternative hypothesis, we can see that there is a greater than symbol, and whenever we have a greater than symbol in the alternative hypothesis, that means that we are doing a right tailed hypothesis test. So we have one critical value, and we can find the critical value by getting the z value that has our alpha as a right tailed probability. You can use either technology or z table, and you will end up getting a critical value of about 2.33, but definitely check to make sure that you do get that value. So that's gonna fall about here, 2.33, our critical value. Now, because we're doing a right tailed hypothesis test, that means that the right tail or the area to the right of our critical value is the rejection region. If we look at our z score, the test statistic, we can see that it is 2.17, which is actually going to be to the left because it's smaller than the critical value. This means that it is not in the rejection region. Great work.

Use α \alpha to find the critical value(s), then determine if the given test statistic is in the rejection region. ( A ) \left(A\right) H 0 : μ = 7.5 ; H a : μ > 7.5 H_0:μ=7.5; H_a:μ>7.5 α = 0.01 ; z = 2.17 α=0.01; z=2.17 Test is [ LEFT | TWO | RIGHT ] -tailed Critical Value(s): Test stat [ IN | NOT IN ] rejection region.

Test is RIGHT -tailed, Critical value(s): 2.33 2.33 2.33 , Test stat NOT IN rejection region.

Test is TWO -tailed, Critical value(s): ± 2.33 \pm2.33 ± 2.33 , Test stat IN rejection region.

Test is LEFT -tailed, Critical value(s): − 2.33 -2.33 − 2.33 , Test stat NOT IN rejection region.

Test is RIGHT -tailed, Critical value(s): 2.17 2.17 2.17 , Test stat IN rejection region.

9. Hypothesis Testing for One Sample

Critical Values and Rejection Regions

Statistics for Business

9. Hypothesis Testing for One Sample

Critical Values and Rejection Regions

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Multiple Choice

Use $α$ to find the critical value(s), then determine if the given test statistic is in the rejection region.
$(A)$ $H_{0} : μ = 7.5; H_{a} : μ > 7.5$
$α = 0.01; z = 2.17$
Test is [ LEFT | TWO | RIGHT ] -tailed
Critical Value(s):
Test stat [ IN | NOT IN ] rejection region.

Test is TWO-tailed, Critical value(s): $\pm2.33$ , Test stat IN rejection region.

Test is LEFT-tailed, Critical value(s): $-2.33$ , Test stat NOT IN rejection region.

Test is RIGHT-tailed, Critical value(s): $2.33$ , Test stat NOT IN rejection region.

Test is RIGHT-tailed, Critical value(s): $2.17$ , Test stat IN rejection region.

Verified step by step guidance

Identify the type of hypothesis test you are conducting (e.g., z-test or t-test) based on the information given or the context of the problem.

Determine the significance level $ \alpha $ for the test, which is the probability of rejecting the null hypothesis when it is true. Common values are 0.05, 0.01, or 0.10.

Find the critical value(s) corresponding to the significance level $ \alpha $ and the type of test (one-tailed or two-tailed). Use the standard normal distribution table for z-tests or the t-distribution table for t-tests. The critical value(s) define the boundary of the rejection region(s).

Define the rejection region(s) based on the critical value(s). For a one-tailed test, the rejection region is either to the left or right of the critical value. For a two-tailed test, the rejection regions are in both tails beyond the positive and negative critical values.

Use the critical value(s) and rejection region(s) to decide whether to reject or fail to reject the null hypothesis by comparing the test statistic to the critical value(s).

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