FedEx and United Parcel Service (UPS) are the world's two...

FedEx and United Parcel Service (UPS) are the world's two leading cargo carriers by volume and revenue (The Wall Street Journal, January 27, 2004). According to the Airports Council International, the Memphis International Airport (FedEx) and the Louisville International Airport (UPS) are 2 of the 10 largest cargo airports in the world. The following random samples show the tons of cargo per day handled by these airports. Data are in thousands of tons. Memphis $$\begin{array}{lrrrrr}9.1 & 15.1 & 8.8 & 10.0 & 7.5 & 10.5 \\ 8.3 & 9.1 & 6.0 & 5.8 & 12.1 & 9.3\end{array}$$ Louisville $$\begin{array}{lllll}4.7 & 5.0 & 4.2 & 3.3 & 5.5 \\ 2.2 & 4.1 & 2.6 & 3.4 & 7.0\end{array}$$ a. Compute the sample mean and sample standard deviation for each airport. b. What is the point estimate of the difference between the two population means? Interpret this value in terms of the higher-volume airport and a comparison of the volume difference between the two airports. c. Develop a $95 \%$ confidence interval of the difference between the daily population means for the two airports.

FedEx and United Parcel Service (UPS) are the world's two leading cargo carriers by volume and revenue (The Wall Street Journal, January 27, 2004). According to the Airports Council International, the Memphis International Airport (FedEx) and the Louisville International Airport (UPS) are 2 of the 10 largest cargo airports in the world. The following random samples show the tons of cargo per day handled by these airports. Data are in thousands of tons.
Memphis $$\begin{array}{lrrrrr}9.1 & 15.1 & 8.8 & 10.0 & 7.5 & 10.5 \\ 8.3 & 9.1 & 6.0 & 5.8 & 12.1 & 9.3\end{array}$$
Louisville $$\begin{array}{lllll}4.7 & 5.0 & 4.2 & 3.3 & 5.5 \\ 2.2 & 4.1 & 2.6 & 3.4 & 7.0\end{array}$$
a. Compute the sample mean and sample standard deviation for each airport.
b. What is the point estimate of the difference between the two population means? Interpret this value in terms of the higher-volume airport and a comparison of the volume difference between the two airports.
c. Develop a $95 \%$ confidence interval of the difference between the daily population means for the two airports.

Key Concepts

Sample Mean

The sample mean is the arithmetic average of a set of numerical observations and serves as an estimate of the central tendency of a population. It is calculated by summing all the observations and dividing by the number of observations, providing a concise summary of the data.

Sample Standard Deviation

The sample standard deviation measures the dispersion or spread of the data around the sample mean. It is obtained by calculating the square root of the variance, which itself is the average of the squared differences between each observation and the sample mean, thereby quantifying variability within the sample.

Point Estimate

A point estimate is a single numerical value used to estimate an unknown population parameter. In comparative studies, the difference between the sample means serves as a point estimate for the difference between the corresponding population means, providing an immediate, though sample-specific, comparison.

Confidence Interval

A confidence interval provides a range of values that is likely to contain the true population parameter with a certain level of confidence (commonly 95%). This interval accounts for sampling variability and offers a measure of the reliability of the point estimate.

Difference Between Two Means

The difference between two means is utilized to compare two populations or groups by calculating the difference between their sample means. This comparison helps in assessing whether there is a meaningful difference in central tendencies between the groups, often accompanied by confidence intervals to express associated uncertainty.

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