Question

Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n = 750 adults over 65 in the study suffer from one or more of the conditions under consideration. Give your answer accurate to three decimal places in decimal form. (Example: 0.398)

Answer 1

Answer:

P ( z )   = 0.005

Step-by-step explanation:

From problem statement:

We know:

Researchers study    45 % adults over 65  suffering disorders

Sample  320   out of 750

then  p =  320 / 750    = 0,4267

1.- Test hypothesis

H₀     null hypothesis                     ⇒     p₀   =  0,45

Hₐ     alternative hypothesis         ⇒     p₀   <  0.45

We calculate the z(s) as:

z(s)  = ( p  -  p₀ )/ √ p₀*q₀/n     ⇒   z(s) = ( 0.4267 - 0.45 )/ √(0.45*0,55)/750 z(s) = - 0.0233* √750 / 0.2475

z(s) = - 0.6381/0.2475       ⇒   z(s) =  - 2.57

We look for - 2.57 in z tabl to find the probability of fewer than 320 out of 750  suffer of disorder, and find

P ( z )   =  0.0051

P ( z )   = 0.005