Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places. e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places. f) Do you reject the null hypothesis? We reject the null hypothesis, since the p-value is less than the significance level. We reject the null hypothesis, since the p-value is not less than the significance level. We fail to reject the null hypothesis, since the p-value is less than the significance level. We fail to reject the null hypothesis, since the p-value is not less than the significance level. g) Select the statement below that best represents the conclusion that can be made. There is sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. There is not sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. The sample data support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. There is not sufficient sample evidence to support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

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

The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to Amercian Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below, which represents the summary statistics for 50 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

n=50; ¯x=40.72 pounds; s=5.03pounds

Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

f) Do you reject the null hypothesis?

We reject the null hypothesis, since the p-value is less than the significance level.
We reject the null hypothesis, since the p-value is not less than the significance level.
We fail to reject the null hypothesis, since the p-value is less than the significance level.
We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

There is sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
There is not sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
The sample data support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
There is not sufficient sample evidence to support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

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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