Suppose we take a random sample of 41 state college students. Then we measure the length of their right foot in centimeters. We compute a 95% confidence interval for the mean foot length for students at this college. We get (21.71, 25.09). Suppose that we now compute a 90% confidence interval. As confidence level decreases, the interval width.

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Mathematics

26 October, 20:28

Suppose we take a random sample of 41 state college students. Then we measure the length of their right foot in centimeters. We compute a 95% confidence interval for the mean foot length for students at this college. We get (21.71, 25.09). Suppose that we now compute a 90% confidence interval. As confidence level decreases, the interval width.

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Nehemiah Nicholson · Answer 1

As confidence level decreases, the interval width decreases too.

Step-by-step explanation:

The confidence interval is an interval in which is probable that the true value of an unknown variable is contained. The confidence level is the probability that this true value is within the limits of the interval.

The degree of confidence or confidence level is defined and affects the width of the confidence interval.

If the true value of the mean foot length is within 21.71 and 25.09 with a 95% confidence level, if we decrease the confidence level to 90%, we expect to have an interval with smaller width.

When we increase the confidence level, we expect to be more sure about the true value being contained in the interval. As we do not count with new information, the only way to be more sure is to have a wider interval.

If the confidence level decreases, we can have a narrower confidence interval as we are not so severe with the probability of containing the true level.