The numbers of successes and the sample sizes are given for independent simple random samples from two populations.Decide whether using the two-proportions z-procedures is appropriate.
-$\mathrm { x } _ { 1 } = 18 , \mathrm { n } _ { 1 } = 30 , \mathrm { x } _ { 2 } = 12 , \mathrm { n } _ { 2 } = 30$
A)Appropriate
B) Not appropriate

Question

Quizplus · Accepted Answer

The two-proportions z-procedure is appropriate when the sample sizes are large enough for the normal approximation to be reasonable. This typically requires that both $np \geq 10$ and $n(1-p) \geq 10$ for each sample. Here, with $x_1 = 18, n_1 = 30$ and $x_2 = 12, n_2 = 30$, both conditions are met for each sample ($18 \geq 10, 12 \geq 10, 30-18=12 \geq 10, 30-12=18 \geq 10$), making the procedure appropriate.

The Numbers of Successes and the Sample Sizes Are Given x1=18,n1=30,x2=12,n2=30\mathrm { x } _ { 1 } = 18 , \mathrm { n } _ { 1 } = 30 , \mathrm { x } _ { 2 } = 12 , \mathrm { n } _ { 2 } = 30x1​=18,n1​=30,x2​=12,n2​=30

The Numbers of Successes and the Sample Sizes Are Given $\mathrm { x } _ { 1 } = 18 , \mathrm { n } _ { 1 } = 30 , \mathrm { x } _ { 2 } = 12 , \mathrm { n } _ { 2 } = 30$