The test statistic of $z=1.80$ is obtained when testing the claim that $p> 0.8$.
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value.
c. Using a significance level of $\alpha=0.10$, 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. This is a right-tailed test.
b. P-value $=\square$ (Round to three decimal places as needed.)
Answer
Final Answer: The P-value is approximately \(\boxed{0.036}\).
Step 1 ：This is a right-tailed test.
Step 2 ：The P-value is the probability that we would observe a test statistic as extreme as, or more extreme than, the one we observed given that the null hypothesis is true. In a right-tailed test, this is the probability that we would observe a test statistic greater than or equal to the one we observed.
Step 3 ：We can find this probability using the standard normal distribution, which gives the probabilities for different z-scores (standard deviations away from the mean). The P-value is 1 minus the cumulative probability up to the observed z-score.
Step 4 ：The P-value is approximately 0.036. This is the probability of observing a test statistic as extreme as, or more extreme than, the one we observed, assuming the null hypothesis is true.
Step 5 ：Final Answer: The P-value is approximately \(\boxed{0.036}\).
