Elly and drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe. using the same data, elly will construct a 90 percent confidence interval and drew will construct a 99 percent confidence interval. which of the following statements is true? a. the midpoint of elly's interval will be greater than the midpoint of drew's interval. b. the midpoint of elly's interval will be less than the midpoint of drew's interval. c. the width of elly's interval will be greater than the width of drew's interval. d. the width of elly's interval will be less than the width of drew's interval. e. the width of elly's interval will be equal to the width of drew's interval

Elly and Drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe.

The width of confidence interval of Elly < The width of confidence interval of Drew because:

The confidence level of Elly  (90%) < The confidence level of Drew (99%)

We can conclude that option d is true which is given by statement

d. The width of Elly's interval will be less than the width of Drew's interval.

Both Elly and Drew are  using the same data.

Elly will construct a 90 % confidence interval.

Drew will construct a 99 % confidence interval.

We have to determine the true statement among the following statements

a. The midpoint of Elly's interval will be greater than the midpoint of Drew's interval.

b. The midpoint of Elly's interval will be less than the midpoint of Drew's interval.

c. The width of Elly's interval will be greater than the width of Drew's interval.

d. The width of Elly's interval will be less than the width of Drew's interval.

e. The width of Elly's interval will be equal to the width of Drew's interval.

A confidence interval expresses a range of values of random variable within which observer is pretty sure that the population parameter lies.

The confidence level shows that how sure the observer is  about the prediction

The more level of confidence includes more number of data, hence wider will be the confidence interval.

So we can conclude that

The width of confidence interval is directly proportional to Level of confidence.

So we can conclude that option d is true which is given by statement

d. The width of Elly's interval will be less than the width of Drew's interval.

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d. The width of Elly's interval will be less than the width of Drew's interval.

Step-by-step explanation:

The confidence level and the width of the confidence interval are direct proportional. This means that a confidence interval with a higher confidence level has a higher width.

For example, a 99 percent confidence interval is wider than a 90 percent confidence interval.

The midpoint of the confidence interval is the mean of the population, no matter the confidence level.

In this problem, we have that:

Elly: 90 percent CI

Drew: 99 percent CI

The correct answer is:

d. The width of Elly's interval will be less than the width of Drew's interval.

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