Question

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming election. A poll of 150 150150 randomly selected voters is taken from the more than 2 , 000 2,0002, comma, 000 voters in the population, and 60 % 60`, percent of those selected plan to vote for the incumbent candidate. The pollster wants to use this data to construct a one-sample z zz interval for a proportion. Which conditions for constructing this confidence interval did their sample meet?

Answer 1

Answer:

$1.\ \ np\geq 10\\\\2.\ \ n\geq 10x$

Step-by-step explanation:

-Let x be the sample size and n the population size

-The conditions for a one-sample proportion z-test are:

-The sample is randomly selected from the population.

-The sample size is greater than or equal to ten times the population size:

$n\geq 10x\\\\n=2000\\x=150\\10x=1500\\\therefore n\geq 10x$

-The expectation np is greater than or equal to 10:

$np\geq 10\\n=2000, p=0.6\\np=1200\\\\Hence, np\geq 10$