Problem

The test statistic of $z=-1.69$ is obtained when testing the claim that $p<0.44$. a. Using a significance level of $\alpha=0.10$, find the critical value(s). b. Should we reject $\mathrm{H}_{0}$ or should we fail to reject $\mathrm{H}_{0}$ ? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a. The critical value(s) is/are $z=$ (Round to two decimal places as needed. Use a comma to separate answers as needed.)

Solution

Step 1 :The test statistic of \(z=-1.69\) is obtained when testing the claim that \(p<0.44\).

Step 2 :Using a significance level of \(\alpha=0.10\), we need to find the critical value(s).

Step 3 :Since the claim is that \(p<0.44\), this is a left-tailed test. Therefore, we need to find the z-score that corresponds to the area to the left under the standard normal curve that equals the significance level of 0.10.

Step 4 :By looking up the z-score in the standard normal distribution table, we find that the critical value is approximately \(-1.28\).

Step 5 :Final Answer: The critical value is \(\boxed{-1.28}\).

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Source: https://solvelyapp.com/problems/7850/

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