Refer to Exercise 32. For each duration, the confidence interval at 40 % 40 % humidity is

Refer to Exercise 32. For each duration, the confidence interval at $40\%$ humidity is narrower than the one at $75\%$ humidity. Which of the following is the best explanation for this?

i. There are more pits at $40\%$ humidity than at $75\%$, and there is greater spread in their depths.

ii. There are fewer pits at $40\%$ humidity than at $75\%$, and there is less spread in their depths.

iii. There are fewer pits at 40\% humidity than at 75\%, and there is greater spread in their depths.

iv. There are more pits at $40\%$ humidity than at $75\%$, and there is less spread in their depths.

Data From Exercise 32:

Refer to the data set pit.csv. Find a confidence interval of the specified level for the mean depth of pits for the following durations and humidity levels. When the sample size is 30 or less, construct a dotplot to determine whether it is appropriate to construct a confidence interval.

Pit Data Set:

In an experiment to measure corrosion in stainless steel, several pieces of stainless steel were exposed to salt particles for various lengths of time, at relative humidities of \(40 \%\) and \(75 \%\). The exposure caused pits to form. After exposure, the depths of the pits were measured, and those greater than \(10 \mu \mathrm{m}\) were reported.
Each row of the data set represents one pit. Variables are the depth of the pit, the duration of exposure, and the relative humidity. Following is a list of the variables in this data set:

Transcribed Image Text:

Duration Humidity Depth Duration of exposure (in weeks) Humidity (in %) Depth of pit (in m)