The following normal quantile plot shows the distribution of the diameters, in cm, of each of nine American Sycamore trees. The normal quantile plot is not linear, which suggests that a transformation...

The following normal quantile plot shows the distribution of the diameters, in cm, of each of nine American Sycamore trees.

The normal quantile plot is not linear, which suggests that a transformation of the data is needed before a confidence interval can be constructed using Student’s t method. The raw data are

12.4 44.8 28.2 77.6 34 17.5 41.5 25.5 27.5

(a) Take the square root of each observation and construct
a 90% confidence interval for the mean.

(b) Interpret the confidence interval from part (a). That
is, explain what the interval tells you about the square
root of the diameters of these trees.