Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table) x₁ = -28.3 x₂ = -18.5 s₁² = 8.7 s₂² = 7.9 n₁ = 22 n₂ = 16 a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
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The pooled variance (s_p^2) is a weighted average of the two sample variances (s_1^2 and s_2^2), where the weights are the sample sizes minus 1. The formula is: s_p^2 = [(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2] / (n_1 + n_2 - 2) Substituting the given values: s_p^2 = Show more…
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Adi S.
Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table) x̄1 = -16.4 x̄2 = -17.1 s1^2 = 8.7 s2^2 = 8.1 n1 = 13 n2 = 25 a. Construct the 99% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is -1.87 to 3.27
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