Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n₁ = 32 and n₂ = 40. The correct distribution to use is the

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When comparing means from two independent samples with unknown variances, the t distribution is used. The degrees of freedom are calculated using a specific formula for unequal sample sizes, which often results in a value less than the sum of the sample sizes minus 2. Here, the degrees of freedom are approximately 70.

Independent Simple Random Samples Are Taken to Test the Difference