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Answer :
We calculate the test statistic with observed data, identify the critical t-value from a t-table, considering a 1% significance level and that it's a two-tailed test. We reject the null hypothesis if our calculated t-value is more extreme than the critical ones.
The subject of this question is the comparison of mean fork lengths of yellowfin tuna from two different zones. To test the marine biologist's claim, we should use the two-sample t-test, as we are comparing means from two independent samples. The null hypothesis (H0) is that the means are equal, and the alternative hypothesis (Ha) is that the means are not equal.
Step 1: Calculate the t-test statistic:
[tex]t = (X1 - X2) / \sqrt((s1^2/n1) + (s2^2/n2))[/tex]
Where X1 and X2 are the sample means, s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes. Insert the given values to get the t-value.
Step 2: Determine the critical t-value using a t-table.
Since the level of significance is 1% and the test is two-tailed (because we're just looking for a 'difference', not a 'greater than' or 'less than' condition), the degree of freedom is (n1+n2-2). Find the associated value from the t-table.
If our calculated t-test statistic falls outside the range of the critical t-values (it is more extreme), we reject the null hypothesis and accept the marine biologists' claim.
Learn more about Two-Sample t-test here:
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