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.
-$$\mathrm { x } _ { 1 } = 14 , \mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 2 } = 3 , \mathrm { n } _ { 2 } = 20$$
A)Appropriate
B) Not appropriate

Question

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.
-$$\mathrm { x } _ { 1 } = 14 , \mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 2 } = 3 , \mathrm { n } _ { 2 } = 20$$  
A)Appropriate
B) Not appropriate

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 means both $np \geq 10$ and $n(1-p) \geq 10$ for both samples. Here, for the first sample, $14$ successes out of $50$ might be okay, but for the second sample, $3$ successes out of $20$ does not meet these conditions, making the procedure not appropriate.

The Numbers of Successes and the Sample Sizes Are Given x1=14,n1=50,x2=3,n2=20\mathrm { x } _ { 1 } = 14 , \mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 2 } = 3 , \mathrm { n } _ { 2 } = 20x1​=14,n1​=50,x2​=3,n2​=20

The Numbers of Successes and the Sample Sizes Are Given $\mathrm { x } _ { 1 } = 14 , \mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 2 } = 3 , \mathrm { n } _ { 2 } = 20$