Answered: Pyramid Lake is on the Paiute Indian…

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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Question

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.

a) State the null and alternate hypotheses. select one:
H0: ? = 19 in; H1: ? > 19 in
H0: ? = 19 in; H1: ? < 19 in
H0: ? < 19 in; H1: ? = 19 in
H0: ? = 19 in; H1: ? ≠ 19 in
H0: ? > 19 in; H1: ? = 19 in

b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student's t, since the sample size is large and ? is unknown.
The standard normal, since the sample size is large and ? is known.
The Student's t, since the sample size is large and ? is known.
The standard normal, since the sample size is large and ? is unknown.

c) What is the value of the sample test statistic? (Round your answer to three decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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