**Understanding Critical Values in Hypothesis Testing**In hypothesis testing, critical values play a vital role in determining the point at which the observed data is considered statistically significant. For any given significance level (often denoted as α), the critical value can be obtained from the standard normal distribution (for Z-tests).*Question:*For the critical value of p = 0.05, what is the z value?Answer: When the significance level (α) is 0.05, this corresponds to a 5% probability in the tails of the standard normal distribution. For a two-tailed test, this means that each tail would have 2.5% (0.025) of the distribution. Using standard normal distribution tables or a calculator, we find that the z value corresponding to 0.025 in one tail is approximately ±1.96.Thus, for p = 0.05, the critical z value is approximately ±1.96.

Answered: For the critical value of p = 0.05,…

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For the critical value of p = 0.05, what is the z value?

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

**Understanding Critical Values in Hypothesis Testing**

In hypothesis testing, critical values play a vital role in determining the point at which the observed data is considered statistically significant. For any given significance level (often denoted as α), the critical value can be obtained from the standard normal distribution (for Z-tests).

*Question:*

For the critical value of p = 0.05, what is the z value?

Answer:

When the significance level (α) is 0.05, this corresponds to a 5% probability in the tails of the standard normal distribution. For a two-tailed test, this means that each tail would have 2.5% (0.025) of the distribution. Using standard normal distribution tables or a calculator, we find that the z value corresponding to 0.025 in one tail is approximately ±1.96.

Thus, for p = 0.05, the critical z value is approximately ±1.96.

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