Bill Alther is a zoologist who studies Anna’s hummingbirds (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:
3.7 2.9 3.8 4.2 4.8 3.1
The sample mean is  = 3.75 grams. Let x be a random variable representing weights of Anna’s hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.70 gram. It is known that for the population of all Anna’s hummingbirds, the mean weight is μ = 4.55 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Use α = 0.01.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.