91Ó°ÊÓ

The Weiss Stats webpage provides the times between eruptions in minutes for $500$ recent observations.

Identify the population.

The population refers to the entire group of persons that are being considered for the study. The population consists of all eruptions of Yellowstone National Park's old faithful geyser.

Variable:

A variable is a measurable attribute or characteristic. Each unit's value for the variable may be different. In other words, a variable is a trait that is recorded for each case. The variable in the study is the "time gap between eruptions (in minutes)."

MINITAB may be used to calculate the $99\%$confidence interval for the mean time between eruptions.

Procedure for MINITAB:

Step 1: Select Stat$>$ Basic Statistics$>$ $1-$Sample $t$ from the drop-down menu.

Step 2: Select Time from the Samples in Column menu.

Step 3: Go to Options and select Confidence Level $99.0$

Step 4: In the alternative, select not equal.

Step 5: In all dialogue boxes, click OK.

MINITAB output:

One-Sample T: TIME

The $99\%$ confidence interval for the MINITAB output is $(90.514,92.642)$

As a result, the $99\%$ confidence interval for the mean time between eruptions is $90.514$ minutes to $92.642$ minutes.

When the sample is collected from the population rather than future data, the confidence interval can be calculated. The confidence interval for future eruptions, say $5$ years away, is meaningless. Furthermore, the current sample does not represent a population in five years because earthquakes and volcanic eruptions are unforeseeable phenomena. This has a greater impact on the interval between eruptions.