The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-test is appropriate.
-$x = 7 , n = 270 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.04 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.04$
A)Not appropriate
B)Appropriate

Question

The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-test is appropriate.
-$x = 7 , n = 270 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.04 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.04$ 
A)Not appropriate
B)Appropriate

Quizplus · Accepted Answer

The one-proportion z-test is appropriate when the sample size is large enough for the sampling distribution of the sample proportion to be approximately normal. This is typically assessed using the np and n(1-p) criteria, where both should be greater than or equal to 10. Given $n = 270$ and $p = 0.04$, $np = 270 \times 0.04 = 10.8$ and $n(1-p) = 270 \times 0.96 = 259.2$, both of which are greater than 10, making the test appropriate.

The Number of Successes and the Sample Size Are Given x=7,n=270,H0:p=0.04,Ha:p≠0.04x = 7 , n = 270 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.04 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.04x=7,n=270,H0​:p=0.04,Ha​:p=0.04

The Number of Successes and the Sample Size Are Given $x = 7 , n = 270 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.04 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.04$