Problem

Find the P-value for the indicated hypothesis test with the given standardized test statistic, $z$. Decide whether to reject $\mathrm{H}_{0}$ for the given level of significance $\alpha$. Right-tailed test with test statistic $z=1.93$ and $\alpha=0.06$ $P$-value $=0.0268$ (Round to four decimal places as needed.) State your conclusion. Fail to reject $\mathrm{H}_{0}$ Reject $\mathrm{H}_{0}$

Solution

Step 1 :Given a right-tailed test with test statistic $z=1.93$ and level of significance $\alpha=0.06$.

Step 2 :The P-value for the test is calculated to be $0.0268$.

Step 3 :The P-value is the probability that, if the null hypothesis were true, we would observe a statistic at least as extreme as the one observed.

Step 4 :To decide whether to reject the null hypothesis, we compare the P-value to the level of significance, $\alpha$. If the P-value is less than $\alpha$, we reject the null hypothesis. If the P-value is greater than $\alpha$, we fail to reject the null hypothesis.

Step 5 :In this case, the P-value is $0.0268$ and $\alpha$ is $0.06$.

Step 6 :Since the P-value is less than $\alpha$, we reject the null hypothesis.

Step 7 :Final Answer: \(\boxed{\text{Reject } H_0}\)

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Source: https://solvelyapp.com/problems/19146/

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