Answered: Bill Alther is a zoologist who studies…

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 σ = 0.62 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.35 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.35 grams? Use ? = 0.01.

(a) What is the level of significance?

State the null hypothesis

H₀

and the alternate hypothesis

H₁

H₀

: μ ---Select--- ≥ = ≠ < > ≤

H₁

: μ ---Select--- ≥ = > ≠ ≤ <

What kind of test is this?

left-tailed testtwo-tailed test right-tailed test

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since n is small with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.

Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)

(c) Find 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 the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion.

There is sufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.35 grams.There is insufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.35 grams.

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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