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5. for the same area you will have a/the t-value, compared to the z-value. a. bigger b. smaller c. same

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As the sample size grows, the t-values approach the z-values. This is due to the fact that as sample sizes increase, the t-distribution converges to the conventional normal distribution. Smaller is the response.

How to determine this

For a given region, a t-value is always less than a z-value. This is because the t-distribution is more dispersed in the tails and flatter in the middle than the conventional normal distribution due to its thicker tails. Because of this, the t-statistic requires a higher absolute value in order to have the same area under the curve as the z-statistic.

For instance, for a sample size of 30, the t-value that corresponds to an area of 0.95 (i.e., 95% of the population falls below this number) is roughly 1.96, but for a sample size of infinity, it is only 1.645. This indicates that with smaller sample sizes, the t-value is lower for the same region.

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