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A medical researcher claims that the average lifespan of a certain species of fish is more than 4 years. A sample of 40 fish is taken and the average lifespan is found to be 4.2 years with a standard deviation of 1.5 years. Can the researcher reject the claim at a significance level of 0.01?

A medical researcher claims that the average lifespan of a certain species of fish is more than 4 years. A sample of 40 fish is taken and the average lifespan is found to be 4.2 years with a standard deviation of 1.5 years. Can the researcher reject the claim at a significance level of 0.01?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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A medical researcher claims that the average lifespan of a certain species of fish is more than 4 years. A sample of 40 fish is taken and the average lifespan is found to be 4.2 years with a standard deviation of 1.5 years. Can the researcher reject the claim at a significance level of 0.01?
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Answer

To perform the hypothesis test, we will use the standard formula for a t-score, which is given by: 

t = (x̄ - μ) / (s/√n) 

where x̄ is the sample mean (4.2), μ is the population mean (4), s is the sample standard deviation (1.5), and n is the sample size (40). 

Plugging in the values, we get: 

t = (4.2 - 4) / (1.5 / √40) = 2.67

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