Question

Check the appropriate conditions for a hypothesis test. Select the correct choice below and fill in the answer boxes within your choice. ​(Round to one decimal place as​ needed.) A. The 416 residents were a random sample from the county of interest. 416 is likely less than​ 10% of the population of a county. One expects np 0equals 74.9 successes and nq 0equals _341 ​failures, which are both more than 10. How did they get 341 failures?

Answer 1

First method

Total number of residents (n) = 416

it is given that np = 74.9, where n = 416 and p = 0.18

{np =74.9, this implies p = 74.9/n and n = 416. So, we get p = 74.9/416 = 0.18}

nq = 341

We know that q = 1- p

and p = 0.18

this implies q = 1-0.18 = 0.82

therefore, n*q = 416*0.82 = 341.12 or 341 (rounded to nearest whole number)

Second method

Total number of residents (n) = 416

we know that success + failures must be equal to 416

let number of failure be x

then

success + x = 416

it is given that success = 74.9 or 75 (rounding to nearest whole number for easy calculation)

this implies

75 + x = 416

subtracting 75 on each side

75 - 75 + x = 416 - 75

this implies

0 + x = 341

or x = 341