Question

3. Let $X_1, dots, X_m$ and $Y_1, dots, Y_n$ be independent random samples from, respectively, a normal ewline $N(mu, sigma^2)$-distribution and a normal $N( u, sigma^2)$-distribution. Determine a confidence interval for ewline $mu - u$ of confidence level $1 - alpha$ ewline (i) if $sigma^2$ is known, ewline (ii) if $sigma^2$ is unknown.

          3. Let $X_1, dots, X_m$ and $Y_1, dots, Y_n$ be independent random samples from, respectively, a normal 
ewline $N(mu, sigma^2)$-distribution and a normal $N(
u, sigma^2)$-distribution. Determine a confidence interval for 
ewline $mu - 
u$ of confidence level $1 - alpha$ 
ewline (i) if $sigma^2$ is known, 
ewline (ii) if $sigma^2$ is unknown.

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3. Let X1, dots, Xm and Y1, dots, Yn be independent random samples from, respectively, a normal
ewline N(mu, sigma^2)-distribution and a normal N(
u, sigma^2)-distribution. Determine a confidence interval for
ewline mu -
u of confidence level 1 - alpha
ewline (i) if sigma^2 is known,
ewline (ii) if sigma^2 is unknown.

Added by Michael S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

07/24/2023

Step 1

Substituting the values for our problem, we get: CI = (X̄ - Ȳ) ± zα/2 * √(σ^2/n) If 0? is unknown, we need to estimate it using the sample variances: s1^2 = (1/n1) * Σ(xi - X̄)^2 s2^2 = (1/n2) * Σ(yi - Ȳ)^2 Show more…

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Let X1, ..., Xm and Y1, ..., Yn be independent random samples from, respectively, a normal N(μ, σ²)-distribution and a normal N(ν, σ²)-distribution. Determine a confidence interval for μ – ν of confidence level 1 – α (i) if σ² is known, (ii) if σ² is unknown.

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