Question 3, 7.2.15
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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 $z=1.28$ and $\alpha =0.07$

P-value $=◻$ (Round to four decimal places as needed.)

Step 1 ：Given a right-tailed test with test statistic $z=1.28$ and significance level $\alpha =0.07$.

Step 2 ：The P-value is the probability that a random variable is more extreme than the observed results, assuming the null hypothesis is true.

Step 3 ：In a right-tailed test, the P-value is the area to the right of the test statistic on the standard normal distribution.

Step 4 ：We can find this value using the cumulative distribution function (CDF) of the standard normal distribution, which gives the probability that a random variable is less than or equal to a given value.

Step 5 ：Since we want the area to the right of the test statistic, we subtract the CDF value from 1.

Step 6 ：The calculated P-value is approximately 0.1003.

Step 7 ：We compare this P-value with the significance level $\alpha =0.07$ to decide whether to reject the null hypothesis.

Step 8 ：If the P-value is less than or equal to $\alpha$, we reject the null hypothesis. Otherwise, we do not reject the null hypothesis.

Step 9 ：The P-value is approximately 0.1003, which is greater than the significance level $\alpha =0.07$. Therefore, we do not reject the null hypothesis.

Step 10 ：Final Answer: The P-value is $\boxed{{\displaystyle 0.1003}}$.