Question

Come up with a variable that is of interest to you. Choose a variable that you can use to estimate the proportion of individuals with that trait or the occurrence of the phenomena.DO NOT USE THE VARIABLE PROVIDED IN THE EXAMPLE BELOW.

For example, suppose you want to estimate the proportion of students at your college who are
left-handed. You decide to collect a random sample of 200 students and ask them which
hand is dominant.

Now, go through the conditions for which all three aspects of the rule for sample proportions apply (picture below) and explain why the rule would apply to this situation for the variable you chose.

Conditions for Which the Rule for Sample Proportions Applies The following three conditions must all be met for the Rule for Sample Pro- portions to apply: 1. There exists an actual population with a fixed proportion who have a cer- tain trait, opinion, disease, and so on. or There exists a repeatable situation for which an outcome of interest is likely to occur with a fixed relative-frequency probability. 2. A random sample is selected from the population, thus ensuring that the probability of observing the characteristic is the same for each sample unit. or The situation is repeated numerous times, with the outcome each time independent of all other times. 3. The size of the sample or the number of repetitions is relatively large. The necessary size depends on the proportion or probability under investiga- tion. It must be large enough so that we are likely to see at least ten with and ten without the specified trait in the sample.

Answer 1

We want to estimate the proportion of employees at our office who have a negative opinion about the current ruling Government. We then decide to collect a random sample of 400 employees and ask them if they had a negative or a positive opinion about the current Government.

Rule applies here as:

1) Proportion is fixed with a population having an opinion.

2) Sample is selected randomly.

3) The sample size is large enough