Question

Please find the limit(s) of the boundaries for the critical region for the following hypotheses (You only need to find the z, t, or F-critical value in all cases, e.g., +/2.33. Please do not complete the hypothesis test):
a. Ho: μd ≤ 6.5, Ha: μd > 6.5, α = 0.05, n = 35, s = 2.5.
b. Ho: μ1 - μ2 ≤ 0, Ha: μ1 - μ2 > 0, α = 0.1, n1 = 13, n2 = 17 (σ1 = σ2).
c. Ho: μ1 - μ2 ≥ 0, Ha: μ1 - μ2 < 0, α = 0.025, n1 = 19, n2 = 27 (σ1 ≠ σ2).
d. Ho: σ12 = σ22, Ha: σ12 ≠ σ22, α = 0.01, n1 = 31, n2 = 21 s1 = 4.1, s2 = 8.3.
e. Ho: σ12 = σ22, Ha: σ12 ≠ σ22, α = 0.05, n1 = 22, n2 = 13 s1 = 7.2, s2 = 10.6.

Answer 1

Answer on Question #60731 – Math – Statistics and Probability

Question

Please find the limit(s) of the boundaries for the critical region for the following hypotheses (You only need to find the z, t, or F-critical value in all cases, e.g., +/2.33. Please do not complete the hypothesis test):

a. Ho: $\mu d \leq 6.5$, Ha: $\mu d > 6.5$, $\alpha = 0.05$, $n = 35$, $s = 2.5$.

b. Ho: $\mu 1 - \mu 2 \leq 0$, Ha: $\mu 1 - \mu 2 > 0$, $\alpha = 0.1$, $n1 = 13$, $n2 = 17$ ($\sigma 1 = \sigma 2$).

c. Ho: $\mu 1 - \mu 2 \geq 0$, Ha: $\mu 1 - \mu 2 < 0$, $\alpha = 0.025$, $n1 = 19$, $n2 = 27$ ($\sigma 1 \neq \sigma 2$).

d. Ho: $\sigma 12 = \sigma 22$, Ha: $\sigma 12 \neq \sigma 22$, $\alpha = 0.01$, $n1 = 31$, $n2 = 21$, $s1 = 4.1$, $s2 = 8.3$.

e. Ho: $\sigma 12 = \sigma 22$, Ha: $\sigma 12 \neq \sigma 22$, $\alpha = 0.05$, $n1 = 22$, $n2 = 13$, $s1 = 7.2$, $s2 = 10.6$.

Solution

a. $t_{crit} = 1.691$

b. $t_{crit} = 1.316$

c. $t_{crit} = -2.064$

d. $F_{crit} = \pm 2.778$

e. $F_{crit} = \pm 2.533$

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