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. 3.7 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 hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.72 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean
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. 3.7 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 hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.72 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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.
3.7 | 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 hummingbirds in this part of the Grand Canyon. We assume that x has a
(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 z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (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.
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: ? = 4.4 g; H1: ? > 4.4 g; right-tailedH0: ? = 4.4 g; H1: ? ≠ 4.4 g; two-tailed H0: ? = 4.4 g; H1: ? < 4.4 g; left-tailedH0: ? < 4.4 g; H1: ? = 4.4 g; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with unknown ?. The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?.
Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (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 ??
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams.There is insufficient evidence at the 0.05 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams.
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