Resolved: How to check critical value from z table ?
I am confused about how I can interpret the critical value from z-table. We know the confidence level, hence we get the level of significance and subsequently the alpha value from it.
Example 95 % confidence, would give us 5% significance and alpha=0.05
Having that one value how can we interpret the critical value?
Example 95 % confidence, would give us 5% significance and alpha=0.05
Having that one value how can we interpret the critical value?
2 answers ( 1 marked as helpful)
Hi Sayantan!
Thanks for reaching out!
To find the critical value using a z-table, start with the confidence level—say, 95%. This means a significance level (α) of 0.05. For a two-tailed test, split this in half (0.05 ÷ 2 = 0.025) and find the cumulative probability (1 - 0.025 = 0.975). Look up 0.975 in the z-table to get the critical value, which is approximately.
For a one-tailed test, use the full α (0.05) and find the cumulative probability (1 - 0.05 = 0.95). Then, look in the z-table for 0.95.
Think of the critical value as the threshold that separates the "unlikely" outcomes from the "likely" ones under the null hypothesis. For example, in a two-tailed test with a 95% confidence level, the critical value is ±1.96. If your test statistic falls beyond these values (greater than 1.96 or less than -1.96), it means the result is in the rejection region, suggesting the outcome is statistically significant (or the result is unlikely to have occurred by chance under the null hypothesis, therefore we can reject it). Essentially, the critical value helps you decide whether to reject the null hypothesis based on where your test statistic lies relative to this threshold.
Hope this helps.
Best,
Ivan
Thanks for reaching out!
To find the critical value using a z-table, start with the confidence level—say, 95%. This means a significance level (α) of 0.05. For a two-tailed test, split this in half (0.05 ÷ 2 = 0.025) and find the cumulative probability (1 - 0.025 = 0.975). Look up 0.975 in the z-table to get the critical value, which is approximately.
For a one-tailed test, use the full α (0.05) and find the cumulative probability (1 - 0.05 = 0.95). Then, look in the z-table for 0.95.
Think of the critical value as the threshold that separates the "unlikely" outcomes from the "likely" ones under the null hypothesis. For example, in a two-tailed test with a 95% confidence level, the critical value is ±1.96. If your test statistic falls beyond these values (greater than 1.96 or less than -1.96), it means the result is in the rejection region, suggesting the outcome is statistically significant (or the result is unlikely to have occurred by chance under the null hypothesis, therefore we can reject it). Essentially, the critical value helps you decide whether to reject the null hypothesis based on where your test statistic lies relative to this threshold.
Hope this helps.
Best,
Ivan
Hi Ivan,
Thanks a lot for your explanation.
Regards,
Sayantan Mukhopadhyay
Thanks a lot for your explanation.
Regards,
Sayantan Mukhopadhyay