According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers wonder if that proportion is now higher, so they take a random sample of 200 homes in California and find that 196 have access to the internet. They want to use this sample data to test H0:p = 0.9 versus Ha:p &gt; 0.9, where p is the proportion of California homes with internet access. Which conditions for performing this type of significance test have been met? Choose all answers that apply. I. The data is a random sample from the population of interest. II. np ≥ 10 and n (1 - p) ≥ 10 III. Individual observations can be considered independent.

Question

According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers wonder if that proportion is now higher, so they take a random sample of 200 homes in California and find that 196 have access to the internet. They want to use this sample data to test H0:p = 0.9 versus Ha:p &amp;gt; 0.9, where p is the proportion of California homes with internet access. Which conditions for performing this type of significance test have been met? Choose all answers that apply. I. The data is a random sample from the population of interest. II. np ≥ 10 and n (1 - p) ≥ 10 III. Individual observations can be considered independent.

Asdrubali2r · Accepted Answer

All three condition conditions will applyCheking for (II) condition. That is  n  p  ≥  10   and   n  (  1  −  p  )  ≥  10    Given   p  =  0.90    n  =  200    n  p  =  200  (  0.90  )    180    &amp;gt;  10    n  (  1  −  p  )  =  200  (  1  −  0.90  )    =  200  (  0.10  )    =  20  &amp;gt;  10When data has random sampling, (I) and (III) condition will automatically met.