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 ? = 0.98 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use ? = 0.01. (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? H0: ? = 4.8 g; H1: ? ≠ 4.8 g; two-tailedH0: ? < 4.8 g; H1: ? = 4.8 g; left-tailed H0: ? = 4.8 g; H1: ? > 4.8 g; right-tailedH0: ? = 4.8 g; H1: ? < 4.8 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 normal distribution and ? = 0.98 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use ? = 0.01.

(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?

H₀: ? = 4.8 g; H₁: ? ≠ 4.8 g; two-tailedH₀: ? < 4.8 g; H₁: ? = 4.8 g; left-tailed H₀: ? = 4.8 g; H₁: ? > 4.8 g; right-tailedH₀: ? = 4.8 g; H₁: ? < 4.8 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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