To determine the P-value and decide whether to reject the null hypothesis $H_0$, we will follow these steps:

Step 1: Identify the Given Information

• Test type: Right-tailed test
• Test statistic (z): $z = 1.00$
• Significance level ($\alpha$): $\alpha = 0.02$

Step 2: Find the P-Value

Since this is a right-tailed test, we want the probability of observing a $z$-value as extreme as or more extreme than 1.00.

Using the standard normal distribution table, we find the area to the right of $z = 1.00$:

• The area to the left of $z = 1.00$ is approximately 0.8413.
• Thus, the area to the right (which is the P-value) is: $P = 1 - 0.8413 = 0.1587$

So, the P-value is approximately 0.1587.

Step 3: Decision Rule

• Compare the P-value with the significance level $\alpha = 0.02$.
• Since $P = 0.1587 > 0.02$, the P-value is greater than $\alpha$, so we fail to reject $H_0$.

Conclusion

With a P-value of 0.1587, which is greater than the 0.02 significance level, we do not have sufficient evidence to reject the null hypothesis $H_0$ at the 0.02 significance level.

Would you like more details, or do you have any questions?

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Here are some related questions:

1. How is the P-value calculated for a two-tailed test?
2. What is the interpretation of failing to reject the null hypothesis?
3. How would the conclusion change if the significance level were 0.10 instead of 0.02?
4. Why is it important to know if a test is right-tailed, left-tailed, or two-tailed?
5. How does changing the test statistic affect the P-value?

Tip: In hypothesis testing, always determine if the test is one-tailed or two-tailed to correctly interpret the P-value.