STATISTICAL TECHNIQUES AND TOOLS
CONFIDENCE INTERVALS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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It reflects greater variability present in small samples.
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It allows us to decrease the margin of error without increasing our confidence level.
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It allows us to use the population standard deviation.
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None of these.
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Detailed explanation-1: -Why do we use a t-distribution instead of a z-distribution for means? It reflects greater variability present in small samples. It allows us to decrease the margin of error without increasing our confidence level.
Detailed explanation-2: -The t-distribution is most useful for small sample sizes, when the population standard deviation is not known, or both. As the sample size increases, the t-distribution becomes more similar to a normal distribution.
Detailed explanation-3: -You must use the t-distribution table when working problems when the population standard deviation () is not known and the sample size is small (n<30). General Correct Rule: If is not known, then using t-distribution is correct. If is known, then using the normal distribution is correct.
Detailed explanation-4: -The t-distribution is used in a confidence interval for a mean when the actual standard error is not known. The t-distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.