Question

A paired difference experiment yielded ${\mathit{n}}_{\mathbf{d}}$pairs of observations. In each case, what is the rejection region for testing ${\mathbf{\text{H}}}_{{}_{\mathbf{\text{0}}}}{\mathbf{\text{:μ}}}_{\mathbf{\text{d}}}\mathbf{\text{>2}}$?

a. ${\mathbf{\text{n}}}_{\mathbf{\text{d}}}\mathbf{\text{=12,α=.05}}$

b.${\mathbf{\text{n}}}_{\mathbf{\text{d}}}\mathbf{\text{=24,α=.10}}$

c.${\mathbf{\text{n}}}_{\mathbf{\text{d}}}\mathbf{\text{=4,α=.025}}$

d.${\mathbf{\text{n}}}_{\mathbf{\text{d}}}\mathbf{\text{=80,α=.01}}$

Short answer

Checking items and paperwork to assess how well demands or criteria are satisfied, finding flaws, measuring excellence as well as danger, establishing trust, and preventing problems.

Step-by-step solution

Step-by-Step Solution Step 1: (a) State the rejection region when  nd= 12, α = 0.05

For a small sample size, the rejection criteria will depend upon the t-test.

Here, $n=12$

So, the degree of freedom will be $n-1=11$

$\alpha =0.05$

So, the upper-tailed test rejection region will be $t>1.796$

(b) State the rejection region when nd= 24, α = 0.10

For a small sample size, the rejection criteria will depend upon the t-test.

Here, $n=24$

So, the degree of freedom will be $n-1=23$

$\alpha =0.10$

So, the upper-tailed test rejection region will be $t>1.319$

(c) State the rejection region when nd= 4, α = 0.025

For a small sample size, the rejection criteria will depend upon the t-test.

Here, $n=4$

So, the degree of freedom will be $n-1=3$

$\alpha =0.025$

So, the upper-tailed test rejection region will be $t>3.181$

(d) State the rejection region when nd= 80, α = 0.01

For a large sample size, the rejection criteria will depend upon the t-test.

Here,$n=80$

So, the degree of freedom will be $=n-1=79$

$\alpha =0.01$

So, the upper-tailed test rejection region will be$t>2.374$