if the test statistic is -4.56 what would the pvalue be

Given that the test statistic is \( z = -4.56 \), we can find the p-value by looking at the standard normal distribution. The p-value corresponds to the probability of observing a test statistic as extreme as -4.56, assuming the null hypothesis is true.

For a \( z \)-value of -4.56, we need to find the area under the standard normal curve to the left of -4.56. Because the standard normal distribution is symmetric, we can use standard normal tables or statistical software to find this value.

In general:

1. For \( z = -4.56 \), the area to the left of this value (which gives us the p-value for a one-tailed test) is extremely small.
2. For a two-tailed test, we double this one-tailed p-value since we are looking at both tails of the distribution.

Using a standard normal distribution table or software, the one-tailed p-value for \( z = -4.56 \) is approximately 0.0000027. 

Therefore, for a two-tailed test:
\[ \text{p-value} = 2 \times 0.0000027 = 0.0000054 \]

### Conclusion

The p-value for a test statistic of \( z = -4.56 \) is approximately 0.0000054. This is an extremely small p-value, which indicates strong evidence against the null hypothesis.

Would you like more details or have any questions about this process?

Here are 5 questions you might ask next:

1. How do I calculate the exact p-value using statistical software?
2. What does a p-value of 0.0000054 mean in practical terms?
3. How does the choice of significance level affect my hypothesis test?
4. What should I do if my sample size is small?
5. Can you explain how to use a normal distribution table to find p-values?

**Tip:** Always double-check if your hypothesis test is one-tailed or two-tailed, as this affects the calculation of the p-value and the conclusion of your test.

Learn how to calculate the p-value for a test statistic of -4.56 in statistics. Understand the concept of standard normal distribution and its application in hypothesis testing. Detailed step-by-step explanation with example calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation