(Solved) When two independent random samples of sizesn1andn2have been selected from populations with ...

When two independent random samples of sizesn₁andn₂have been selected from populations with meansμ₁andμ₂and variances

$\style{font-family:Times New Roman;}{\sigma_1^2}$ and

$\style{font-family:Times New Roman;}{\sigma_2^2,}$ which of the following statements is true?

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If the sampled populations are normally distributed, then the sampling distribution of $\style{font-family:Times New Roman;}{{\overline x}_1-{\overline x}_2}$ is exactly normal only whenn₁andn₂are both at least 30.

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If the sampled populations are normally distributed, then the sampling distribution of $\style{font-family:Times New Roman;}{{\overline x}_1-{\overline x}_2}$ is normal regardless of the sample sizes.

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If the sampled populations arenotnormally distributed, then the sampling distribution of $\style{font-family:Times New Roman;}{{\overline x}_1-{\overline x}_2}$ is normal regardless of the sample sizes.

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If the sampled populations are normally distributed, then the sampling distribution of $\style{font-family:Times New Roman;}{{\overline x}_1-{\overline x}_2}$ is approximately normal only ifn₁+n₂≥ 30.

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When two independent random samples of sizesn1andn2have been selected from populations with ...

Introductory Statistics: A Problem-Solving Approach

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