The relationship between length and height for 147 male guppies was introduced in Exercise 6.10, which used the summary statistics to calculate the equation of the least squares line for length as a function of height and estimate the mean length of an adult male guppy with height \(180 \mathrm{~cm}\). The estimated residual standard error from this model is \(s=50.93\).

(a) Use the summary statistics given in Exercise 6.10 to construct a 95% confidence interval for the estimated mean length when height is \(180 \mathrm{~cm}\).

(b) Use a prediction interval based on the summary statistics to estimate the lengths for a new \(180 \mathrm{~cm}\) guppy that would be more than two standard deviations above and below the estimated mean.

(c) Use the approximate formulas for the standard error for a mean and for a prediction to recalculate the intervals in parts (a) and (b).

Data From Exercise 6.10

Transcribed Image Text:

6.10 Guppies, Part I. Guppies are small, brightly colored tropical fish often seen in freshwater fish aquar- iums. A study was conducted in 147 male guppies to examine the relationship between coloration and het- erozygosity; heterozygosity refers to the condition of having different alleles at a given genetic locus. The guppies were randomly sampled from a river in the wild. In an initial stage of the study, researchers examined whether length and height are linearly associated. The mean length is 1261.21 cm, with standard deviation 95.62 cm. The mean height is 201.75 cm, with stan- dard deviation 20.68. The correlation between length and height is 0.85.