Question

Suppose \{X_{11}, X_{12},...,X_{1m}\} iid N(\mu_1, \sigma^2) \{X_{21}, X_{22},...,X_{2n}\} iid N(\mu_2, \sigma^2) \mu_1 \& \mu_2 unknown, \sigma_1^2 = \sigma_2^2 = 16 n_1 = n_2 = 36 \bar{X}_1 = 41 \qquad \bar{X}_2 = 42 Test \ the \ hypotheses H_0: \mu_1 = \mu_2 \qquad \alpha = .05 H_0: \mu_1 < \mu_2 A. What is prob of Type 1 error ? B. what is prob of Type 2 error if \mu_1 = 40 \& \mu_2 = 41 ? C. In part B, what if n_1 = n_2 = 64?

          Suppose \{X_{11}, X_{12},...,X_{1m}\} iid N(\mu_1, \sigma^2)
\{X_{21}, X_{22},...,X_{2n}\} iid N(\mu_2, \sigma^2)
\mu_1 \& \mu_2 unknown, \sigma_1^2 = \sigma_2^2 = 16
n_1 = n_2 = 36
\bar{X}_1 = 41 \qquad \bar{X}_2 = 42
Test \ the \ hypotheses
H_0: \mu_1 = \mu_2 \qquad \alpha = .05
H_0: \mu_1 < \mu_2
A. What is prob of Type 1 error ?
B. what is prob of Type 2 error if
\mu_1 = 40 \& \mu_2 = 41 ?
C. In part B, what if n_1 = n_2 = 64?

$Suppose {X11, X12,...,X1m} iid N(μ1, σ^2) {X21, X22,...,X2n} iid N(μ2, σ^2) μ1 & μ2 unknown, σ1^2 = σ2^2 = 16 n1 = n2 = 36 X̅1 = 41 X̅2 = 42 Test the hypotheses H0: μ1 = μ2 α= .05 H0: μ1 < μ2 A. What is prob of Type 1 error ? B. what is prob of Type 2 error if μ1 = 40 & μ2 = 41 ? C. In part B, what if n1 = n2 = 64?$

Added by Wendy V.

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