Using the data from Problem 7, test whether the standard deviation of acidity in the rain near Houston, Texas, is different from that near Chicago, Illinois, at the \(\alpha=0.05\) level of significance.

Data from Problem 7

A researcher wants to know whether the acidity of rain \((\mathrm{pH})\) near Houston, Texas, is significantly different from that near Chicago, Illinois. He randomly selects 12 rain dates in Texas and 14 rain dates in Illinois and obtains the following data:

Is the sampling method dependent or independent? Why?

Because the sample sizes are small, what must be true regarding the populations from which the samples were drawn?

Draw side-by-side boxplots of the data. What does the visual evidence imply about the \(\mathrm{pH}\) of rain in the two states?

Does the evidence suggest that there is a difference in the \(\mathrm{pH}\) of rain in Chicago and Houston? Use the \(\alpha=0.05\) level of significance.