When testing H₀ : μ₁ - μ₂ = 0 against H₁ : μ₁ - μ₂ ≠ 0,the observed value of the Z-score was found to be -2.13.The p-value for this test would be 0.4668.

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The p-value for a Z-score of -2.13 in a two-tailed test is approximately 0.0332, not 0.4668. This is because the Z-score indicates how many standard deviations an element is from the mean, and a Z-score of -2.13 corresponds to a p-value that reflects the probability of observing such a result under the null hypothesis. The p-value is found by looking up the Z-score in a standard normal distribution table or using a statistical software, and it represents the area under the curve to the extremes of the distribution. For a two-tailed test, you would look at both tails of the distribution.

When Testing H0 : μ1 - μ2 = 0 Against

When Testing H₀ : μ₁ - μ₂ = 0 Against