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?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Question
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?
Expert Solution
Step 1
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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