Suppose that county planners are interested in learning about the proportion of county residents who would pay a fee for a curbside recycling service if the county were to offer this service. Two different people independently selected random samples of county residents and used their sample data to construct the following confidence intervals for the proportion who would pay for curbside recycling. Interval 1: (0.62, 0.68) Interval 2: (0.62, 0.66) (a) Explain how it is possible that the two confidence intervals are not centered in the same place. The two samples have different margins of error.The two samples have different sizes. Different confidence levels were used for the two intervals.The two samples were taken from different populations.The two samples have different sample proportions. (b) Which of the two intervals conveys more precise information about the value of the population proportion? Interval 1Interval 2 (c) If both confidence intervals are associated with a 95% confidence level, which confidence interval was based on the smaller sample size? Interval 1Interval 2 How can you tell? A smaller sample size produces a margin of error. (d) If both confidence intervals were based on the same sample size, which interval has the higher confidence level? Interval 1Interval 2 How can you tell? The z critical value for higher confidence is , resulting in a confidence interval.

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Description: Suppose that county planners are interested in learning about the proportion of county residents who would pay a fee for a curbside recycling service if the county were to offer this service. Two different people independently selected random samples

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that county planners are interested in learning about the proportion of county residents who would pay a fee for a curbside recycling service if the county were to offer this service. Two different people independently selected random samples of county residents and used their sample data to construct the following confidence intervals for the proportion who would pay for curbside recycling.

Interval 1:	(0.62, 0.68)
Interval 2:	(0.62, 0.66)

(a)

Explain how it is possible that the two confidence intervals are not centered in the same place.

The two samples have different margins of error.The two samples have different sizes. Different confidence levels were used for the two intervals.The two samples were taken from different populations.The two samples have different sample proportions.

(b)

Which of the two intervals conveys more precise information about the value of the population proportion?

Interval 1Interval 2

(c)

If both confidence intervals are associated with a 95% confidence level, which confidence interval was based on the smaller sample size?

Interval 1Interval 2

How can you tell?

A smaller sample size produces a margin of error.

(d)

If both confidence intervals were based on the same sample size, which interval has the higher confidence level?

Interval 1Interval 2

How can you tell?

The z critical value for higher confidence is , resulting in a confidence interval.

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