Reference no: EM132857547
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna3.7 2.9 3.8 4.2 4.8 3.1). (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.
The sample mean is = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? 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?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
(e) State your conclusion in the context of the application.
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: Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna3.7 2.9 3.8 4.2 4.8 3.1). (Reference: Hummingbirds, K. Long, W. Alther.)
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