Question: 1. A question relating to a study of the echolocation system for bats is how far apart the bat and an insect are when the

1. A question relating to a study of the echolocation system for bats is how far apart the bat and an insect are when the bat first senses the insect. The technical problems for measuring this are complex and so only n = 11 data points were obtained (in dm):

x 57.16, 48.42, 46.84, 19.62, 41.72, 36.75, 62.69, 48.82, 36.86, 50.59, 47.53 It is given that X = 45.18 and S = 11.48.

(a) Construct by hand a 95% CI for the mean distance μ.

What assumptions, if any, are needed for the validity of this CI?

(b) Copy the data into theRobject x, that is, by x=c(57.16, 48.42, 46.84, 19.62, 41.72, 36.75, 62.69, 48.82, 36.86, 50.59, 47.53), and do the normal Q-Q plot for this data. Comment on the appropriateness of the CI in part (a).

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