Question

1. A survey selects a simple random sample of n= 500 people from a town of 55,000. The sample shows a mean of 2.3 health problems per person. Based on this information, say whether each of the following statements is true or false. Explain your reasoning in each instance. No calculations are necessary.

1. It is reasonable to assume that the number of health problems per person will vary according to a normal distribution.

2. It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution.

Answer 1

a. True

Each person has a probability of having health problems because, mean is 2.3. It is showing that even at worst case each person have a chance of having atleast one health issue. It also doesn't mean that health issues are uniformly distributed. There are some persons having more health issues and some having less. But, it happens with everyone goes on with infinite random person. So, it is perfect example of normal distribution.

b. False

Sample selection and it's characteristics are different from each other. Their means and deviations are different from sample to sample. For every random sample, characteristics vary. Moreover their variation is not continuous.