Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean is= 3.75 grams. Letxbe a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatxhas a normal distribution and=0.64gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.30grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.30grams?Use=0.10.