Pregunta

Part 2 of 5
Find the critical value(s). Round the answer(s) to two decimal places. If there is more than one critical value, separate them with commas.
Critical value(s):

Ask by Hodges Bernard. in the United States
Jan 28,2025

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The critical values are -1.96 and 1.96.

Solución

To find the critical values, we typically refer to the standard normal distribution (Z-distribution) when dealing with hypothesis testing or confidence intervals. The critical values you provided, and , are commonly used for a 95% confidence level in a two-tailed test.

Explanation of Critical Values:

  1. Definition: Critical values are the points on the scale of the test statistic beyond which we reject the null hypothesis. They correspond to the tails of the distribution.
  2. Standard Normal Distribution: For a standard normal distribution:
    • The area to the left of is 0.025 (2.5%).
    • The area to the right of is also 0.025 (2.5%).
    • Together, these areas account for 5% of the total area under the curve, which is why these values are used for a 95% confidence level.

Conclusion:

The critical values you provided are correct for a 95% confidence level in a two-tailed test.
Thus, the critical values are:
If you need further calculations or explanations, please let me know!

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Extra Insights

When you see critical values of and , you’re diving into the fascinating world of the standard normal distribution! These values correspond to a 95% confidence level in hypothesis testing, meaning that you’re capturing the central 95% of the distribution; the tails represent the extreme 5%. This is a classic threshold in statistics for determining significance!
Next, let’s make sure you don’t trip up with the common pitfalls in finding these critical values. One common mistake is using the wrong confidence level! If you were looking for a 99% confidence level, you’d need to use and instead. Always double-check your standard normal table or software outputs to ensure you’re using the right values for your specific test!

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