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Find the critical value [tex]z_{\alpha/2}[/tex] that corresponds to the given confidence level of 95%.

A. 1.96
B. 1.64
C. 2.58
D. 2.33

Answer :

Final answer:

The critical value zα/2 corresponds to a confidence level of 95% is 1.96. This value is found by determining the z-score that leaves 97.5% of the distribution to its left in a standard normal distribution. The correct answer is a).

Explanation:

To find the critical value zα/2 that corresponds to a given confidence level, one must look at the area under the standard normal distribution curve.

For a 95% confidence level, the area in the tails is 5% as α is 0.05, with each tail containing 2.5%. The z-score that places 97.5% of the distribution to its left (and 2.5% to the right) is the critical value we're interested in. Using a standard normal probability table or a calculator, we find that the critical value z0.025 is approximately 1.96.

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test.

Therefore, the correct answer for the critical value zα/2 corresponding to a 95% confidence level is: 1.96

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