An automobile manufacturer wants to estimate the mean...

An automobile manufacturer wants to estimate the mean gasoline mileage of its new compact model. How many sample runs must be performed to ensure that the estimate is accurate to within 0.3 mpg at $95 \%$ confidence? (Assume $\sigma=1.5 .$ )

Key Concepts

Confidence Interval

A confidence interval provides a range of values that is likely to contain the population parameter, such as the mean, with a certain level of confidence (e.g., 95%). It is constructed from sample data, and the width of the interval reflects the uncertainty associated with the estimate of the population parameter.

Margin of Error

The margin of error is the maximum expected difference between the true population parameter and a sample estimate. It is determined by the critical value from the relevant probability distribution (e.g., the z-score for a normal distribution), the population standard deviation, and the sample size, and it dictates how precise an estimate is.

Z-Critical Value

The z-critical value is a point on the standard normal distribution that corresponds to the desired level of confidence. In constructing confidence intervals, it defines the number of standard deviations a data point is from the mean for a given confidence level, such as 1.96 for a 95% confidence interval.

Sample Size Calculation

Sample size calculation involves determining the number of observations required to achieve a desired margin of error at a given confidence level. When the population standard deviation is known, this calculation typically uses the formula n = (z*sigma/E)^2, ensuring that the estimate is precise enough for the desired level of accuracy.

Transcript

Please give Ace some feedback