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Ch. 6 - Confidence Intervals
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 6 - Confidence IntervalsProblema 6.3.20a
Capitolo 6, Problema 6.3.20a

Alcohol-Impaired Driving You wish to estimate, with 95% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. Your estimate must be accurate within 5% of the population proportion.
a. No preliminary estimate is available. Find the minimum sample size needed

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Determine the formula for the minimum sample size required to estimate a population proportion with a given margin of error. The formula is: nmin = z2E² × 0.25, where z is the z-score corresponding to the confidence level, E is the margin of error, and 0.25 is used when no preliminary estimate is available.
Identify the z-score for a 95% confidence level. For a 95% confidence level, the z-score is approximately 1.96. This value corresponds to the critical value of the standard normal distribution for a two-tailed test.
Substitute the margin of error (E) into the formula. The problem specifies that the estimate must be accurate within 5%, so E = 0.05.
Substitute the values of z and E into the formula: nmin = 1.9620.05² × 0.25.
Simplify the expression to calculate the minimum sample size. Ensure that the result is rounded up to the nearest whole number, as sample size must be a whole number.

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Population Proportion

The population proportion refers to the fraction of a population that exhibits a certain characteristic, in this case, the proportion of motor vehicle fatalities caused by alcohol-impaired driving. Understanding this concept is crucial for estimating how widespread an issue is within a larger group, which informs decisions and policies.
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Constructing Confidence Intervals for Proportions

Sample Size Determination

Sample size determination is the process of calculating the number of observations or replicates needed to ensure that the sample accurately reflects the population. In this context, it involves using statistical formulas to find the minimum number of fatalities required to estimate the population proportion with a specified level of confidence and margin of error.
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Coefficient of Determination

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the population parameter with a specified level of confidence, such as 95%. This concept is essential for understanding the reliability of the estimate, as it indicates how much uncertainty is associated with the sample data.
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Introduction to Confidence Intervals
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