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For the same sample size, a lower level of precision in a confidence interval (i.e. a larger margin of error, a larger sampling error or a wider confidence interval) results from having ______

(1) a larger sampling distribution.
(2) a smaller sampling distribution.
(3) a higher level of confidence.
(4) a smaller sample mean.
(5) a smaller population variance.

Respuesta :

Answer:

Correct option: (3) a higher level of confidence.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population parameter is:

CI = Sample Statistic ± [Critical Value × (Standard deviation/ √Sample size)]

The margin of error of the confidence interval is:

MOE = [Critical Value × (Standard deviation/ √Sample size)]

The MOE is dependent on:

  1. Confidence level
  2. Standard deviation
  3. Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the  confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

If the sample size is not altered, then the widening of the confidence interval can because of two reasons:

  1. The confidence level was increased, thus increasing the critical value.
  2. The standard deviation was increased.

The correct option in this case is (3) a higher level of confidence.

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