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Ch. 7 - Estimating Parameters and Determining Sample Sizes
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 7, Problem 7.1

Female Motorcycle Owners Here is a 95% confidence interval estimate of the percentage of motorcycle owners who are female: 17.5%<p<20.6% (based on data from the Motorcycle Industry Council). What is the best point estimate of the percentage of motorcycle owners who are women?

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1
Identify the given confidence interval for the percentage of motorcycle owners who are female: 17.5% < p < 20.6%.
Recall that the best point estimate for a population proportion is the midpoint of the confidence interval.
To find the midpoint, use the formula: \( \text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} \).
Substitute the given values into the formula: \( \text{Midpoint} = \frac{17.5 + 20.6}{2} \).
Simplify the expression to calculate the best point estimate of the percentage of motorcycle owners who are women.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, such as 95%. In this case, the interval estimates the percentage of female motorcycle owners, indicating that we can be 95% confident that the true percentage lies between 17.5% and 20.6%.
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Introduction to Confidence Intervals

Point Estimate

A point estimate is a single value that serves as a best guess or approximation of a population parameter. In the context of the given confidence interval, the best point estimate for the percentage of female motorcycle owners can be calculated as the midpoint of the interval, providing a concise representation of the data.
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Introduction to Confidence Intervals

Population Proportion

The population proportion refers to the fraction of a population that possesses a certain characteristic, in this case, being female motorcycle owners. Understanding this concept is crucial for interpreting the confidence interval and point estimate, as it reflects the actual percentage of interest within the broader population of motorcycle owners.
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Constructing Confidence Intervals for Proportions
Related Practice
Textbook Question

Sample Size for Mean Find the sample size required to estimate the mean IQ of airline pilots. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that sigma=15

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Textbook Question

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.


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Textbook Question

Determining Sample Size. Assume that each sample is a simple random sample obtained from a normally distributed population.


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Textbook Question

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Textbook Question

use the given information to find the number of degrees of freedom, the critical values X2L and X2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution:


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Textbook Question

One-Sided Confidence Interval A one-sided claim about a population proportion is a claim that the proportion is less than (or greater than) some specific value. Such a claim can be formally addressed using a one-sided confidence interval for p, which can be expressed as p<p+E or p>p-E, where the margin of error E is modified by replacing za/2 with za. (Instead of dividing between two tails of the standard normal distribution, put all of it in one tail.) The Chapter Problem refers to a Sallie Mae survey of 950 undergraduate students, and 53% of the survey subjects take online courses. Use that data to construct a one-sided 95% confidence interval that would be suitable for helping to determine whether the percentage of all undergraduates who take online courses is greater than 50%.

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