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.3.72.93.84.24.83.1The 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.(a)What is the level of significance? (Enter a number.)

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀:?= 4.3 g;H₁:?

H₀:?H₁:?= 4.3 g; left-tailed

H₀:?= 4.3 g;H₁:??4.3 g; two-tailed

H₀:?= 4.3 g;H₁:?> 4.3 g; right-tailed

(b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student'st, since we assume thatxhas a normal distribution with known?.

The Student'st, sincenis large with unknown?.

The standard normal, since we assume thatxhas a normal distribution with known?.

The standard normal, since we assume thatxhas a normal distribution with unknown?.

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

(c)Find (or estimate) theP-value. (Enter a number. Round your answer to four decimal places.)

**see attached picture for 2nd part of this problem**

\f