In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results: x1 and x2 are sample means; s1 and s2 are sample deviations.Sample 1Sample 2X1 = 6,275X2 = 6,840S1 = 350S2 = 250Use a 99% confidence interval to estimate the difference between the population means (μ1 – μ2). Interpret the confidence interval.Test the null hypothesis H0: (μ1 – μ2) = 0 versus the alternative hypothesis Ha: ((μ1 – μ2) ≠ 0. Give the significance level of the test and interpret the result.Suppose the test in part b was conducted with the alternative hypothesis Ha: (μ1 – μ2) > 0. How would your answer to part b change?Test the null hypothesis H0: (μ1 – μ2) = 25 versus Ha: (μ1 – μ2) ≠ 25. Give the significance level and interpret the result. Compare your answer to the test conducted in part b.What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a-d?

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Answered: Suppose the test in part b was…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results: x1 and x2 are sample means; s1 and s2 are sample deviations.

Sample 1	Sample 2
X₁ = 6,275	X₂ = 6,840
S₁ = 350	S₂ = 250

Use a 99% confidence interval to estimate the difference between the population means (μ_{1 –}μ₂). Interpret the confidence interval.
Test the null hypothesis H₀: (μ_{1 –}μ₂) = 0 versus the alternative hypothesis H_a: ((μ_{1 –}μ₂) ≠ 0. Give the significance level of the test and interpret the result.
Suppose the test in part b was conducted with the alternative hypothesis H_a: (μ_{1 –}μ₂) > 0. How would your answer to part b change?
Test the null hypothesis H₀: (μ_{1 –}μ₂) = 25 versus H_a: (μ_{1 –}μ₂) ≠ 25. Give the significance level and interpret the result. Compare your answer to the test conducted in part b.
What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a-d?

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