about 32% of the population in a large region are between the ages of 40 and 65, according to the countrys…

about 32% of the population in a large region are between the ages of 40 and 65, according to the countrys census. however, only 2% of the 2700 employees at a company in the region are between the ages of 40 and 65. lawyers might argue that if the company hired people regardless of their age, the distribution of ages would be the same as though they had hired people at random from the surrounding population. check whether the conditions for using the one - proportion z - test are met. are all the conditions satisfied? select all that apply. a. no, the large sample size condition is not satisfied or cannot be reasonably assumed. b. no, the independence condition is not satisfied or cannot be reasonably assumed. c. no, the large population condition is not satisfied or cannot be reasonably assumed. d. no, the random sample condition is not satisfied or cannot be reasonably assumed. e. yes, all conditions are satisfied or can be reasonably assumed.

about 32% of the population in a large region are between the ages of 40 and 65, according to the countrys census. however, only 2% of the 2700 employees at a company in the region are between the ages of 40 and 65. lawyers might argue that if the company hired people regardless of their age, the distribution of ages would be the same as though they had hired people at random from the surrounding population. check whether the conditions for using the one - proportion z - test are met. are all the conditions satisfied? select all that apply. a. no, the large sample size condition is not satisfied or cannot be reasonably assumed. b. no, the independence condition is not satisfied or cannot be reasonably assumed. c. no, the large population condition is not satisfied or cannot be reasonably assumed. d. no, the random sample condition is not satisfied or cannot be reasonably assumed. e. yes, all conditions are satisfied or can be reasonably assumed.

Answer

Brief Explanations:

  1. Random Sample condition: There is no indication that the 2700 employees are a random sample from the surrounding population. We don't know how the employees were hired, so this condition is not satisfied.
  2. Independence condition: We assume that the age - status of one employee does not affect the age - status of another employee. Since we are dealing with a large number of employees (2700), this condition can be reasonably assumed.
  3. Large Sample Size condition: $np = 2700\times0.02=54$ and $n(1 - p)=2700\times(1 - 0.02)=2700\times0.98 = 2646$. Since $np\geq10$ and $n(1 - p)\geq10$, this condition is satisfied.
  4. Large Population condition: The population of the large region is likely much larger than the sample of 2700 employees. So this condition is satisfied.

Answer:

D. No, the Random Sample condition is not satisfied or cannot be reasonably assumed.