Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).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.3.72.93.84.24.83.1The sample mean isx= 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=0.82gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.50grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.50grams?Use=0.10.

(a) Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)

(b) Find (or estimate) theP-value. (Round your answer to four decimal places.)