How to find p value given z on TI-83?

How to find p value given z on TI-83?

When conducting statistical analyses, determining the p-value is a crucial step to make informed decisions and draw accurate conclusions. The p-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. The TI-83 calculator provides a convenient way to compute the p-value given a z-score. Here’s a step-by-step guide on how to find the p-value using a TI-83 calculator:

1. Turn on the calculator and select the “DISTR” key, which is located above the “VARS” key.
2. Scroll down to locate and select the “invNorm” function.
3. You will see a prompt with the form “invNorm(area to the left, mean, standard deviation).” Here’s where we enter the information required to find the p-value.
4. Input the area to the left of the z-score, which is the probability of observing a value less than the given z-score. This area is typically denoted as α, the significance level or the alpha level.
5. For a two-tailed test (where the null hypothesis is not one-sided), divide the significance level by 2 to account for the area in both tails. For example, if α = 0.05, enter 0.05/2 = 0.025.
6. The mean and standard deviation are usually not necessary for finding the p-value using the z-score. Hence, you can leave these values blank (just press the comma key or “2nd,” followed by the comma key twice) since the standard normal distribution has a mean of 0 and a standard deviation of 1.
7. Press the “Enter” key, and the calculator will provide the z-score corresponding to the probability entered in Step 4.
8. To find the p-value, subtract the obtained z-score from 1. This is because the area under the curve always sums up to 1, and we are interested in the probability in the tail(s) beyond the z-score.
9. Round the p-value to the desired decimal places for better interpretability.

**Ultimately, to find the p-value given a z-score on a TI-83 calculator, follow these steps:**
1. Press “DISTR” and select “invNorm.”
2. Enter the area to the left of the z-score or significance level.
3. Leave the mean and standard deviation fields blank.
4. Press “Enter” to find the corresponding z-score.
5. Subtract the obtained z-score from 1 to find the p-value.
6. Round the p-value to the desired decimal places.

FAQs:

1. What is a p-value?

The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true.

2. What does the p-value signify?

The p-value helps determine the statistical significance of the observed data. A small p-value (less than the chosen significance level) suggests that the observed evidence is unlikely to occur by chance, leading to rejection of the null hypothesis.

3. How do I interpret the p-value?

If the p-value is less than the chosen significance level (commonly 0.05), it suggests strong evidence against the null hypothesis. On the other hand, a p-value greater than the significance level indicates insufficient evidence to reject the null hypothesis.

4. What is a z-score?

A z-score is a standardized score that represents the number of standard deviations an observed value deviates from the mean.

5. When should I perform a one-tailed versus a two-tailed test?

A one-tailed test is appropriate when investigating a specific direction (e.g., testing if the mean is greater than a certain value), while a two-tailed test is used to assess significance in both tails (e.g., testing if the mean is not equal to a certain value).

6. Can I compute the p-value directly on a TI-83 calculator?

The TI-83 calculator does not directly provide the p-value for a given z-score. However, you can compute it by subtracting the obtained z-score from 1.

7. What is the significance level (alpha level)?

The significance level, commonly denoted as α, is the threshold at which the p-value determines the statistical significance of the result. It helps determine if the observed evidence is significant enough to reject the null hypothesis.

8. What if my p-value is less than 0.001?

When the p-value is extremely small (e.g., less than 0.001), it indicates highly significant evidence against the null hypothesis.

9. Can I find the p-value for other statistical tests using the TI-83 calculator?

While the TI-83 calculator is widely used for basic statistical analyses and hypothesis testing, it might have limitations when performing advanced tests. For more complicated tests or functions, it is recommended to utilize specialized statistical software or consult a statistician.

10. Are there other methods to calculate the p-value?

Yes, besides using calculators, p-values can also be calculated manually using tables for specific distributions or by employing statistical software that provides more comprehensive statistical analysis.

11. Can I find the p-value for non-standard normal distributions?

For distributions other than the standard normal distribution, the TI-83 calculator cannot directly calculate the p-value. In such cases, you may need to use statistical tables or specialized software that supports the specific distribution you are working with.

12. Can I find confidence intervals using the TI-83 calculator?

Yes, the TI-83 calculator can calculate confidence intervals for means or proportions by utilizing the “ZInterval” function in the “STAT” menu. However, this function requires the sample mean, standard deviation (or proportion), sample size, and desired confidence level as inputs.

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