Section 9.1 #21 Complete the full hypothesis test for the question below. All parts must be shown. Label each part. For full credit be sure to include the null and alternative hypothesis, type of test, critical value, where shaded on curve, test statistic, conclusion, statement about the conclusion.

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna; Reference:Hummingbirdsby K. Long and 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

3.7 2.9 3.8 4.2 4.8 3.1

The sample mean is X = 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 o = 0.70 grams. It is known that for the population of all Anna's hummingbirds, the mean weight is u = 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 a = 0.01