Hypothesis Testing: Computing the z-value and Confidence Interval | Test Prep

Where will 97% of the computed z-value lie between?

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Question

If the null hypothesis that two means are equal is in fact true, where will 97% of the computed z-value lie between?

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A. B. C. D. E.

C

From the z tables, we can find 0.97/2 = 0.485, which corresponds to a z-value of +/-2.17.

To answer this question, we need to consider the critical value of the z-statistic for a 97% confidence level. The z-value represents the number of standard deviations away from the mean.

In hypothesis testing, the null hypothesis states that there is no significant difference between the means of two groups. If the null hypothesis is true, the computed z-value will follow a standard normal distribution.

For a two-tailed test (which is appropriate in this case since we're considering "between" two means), the critical value is determined by dividing the significance level (1 - confidence level) equally between the two tails of the distribution.

For a 97% confidence level, the significance level is 1 - 0.97 = 0.03. Since we divide it equally between the two tails, each tail has an area of 0.03/2 = 0.015.

To find the z-value corresponding to this area, we can consult a standard normal distribution table or use statistical software. The z-value for an area of 0.015 (in either tail) is approximately ±2.17.

Therefore, the correct answer is C. +/- 2.17.