If the mean and trimmed mean are nearly identical, it might be thought that it makes little difference which measure of location is used. Based on your answer to given Exercise 1, why might it make a difference?
Exercise 1
In Exercise 2, the length of the confidence interval for µ is 257.6 - 200.7 = 56.9 and the length based on the trimmed mean is 244.9 - 196.7 = 48.2. Comment on why the length of the confidence interval for the trimmed mean is shorter.
Exercise
Reported data on the number of seeds in 29 pumpkins. The results were
250, 220, 281, 247, 230, 209, 240, 160, 370, 274, 210, 204, 243, 251, 190, 200, 130, 150, 177, 475, 221, 350, 224, 163, 272, 236, 200, 171, 98.
The 20% trimmed mean is X‾t = 220.8 and the mean is X‾= 229.2. Verify that the .95 confidence interval for µ is (200.7, 257.6) and that for the trimmed mean, µt, it is (196.7, 244.9).