Question

Use the following information to answer the next five exercises: A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important. Using Excel and functions. Don't forget to use this formula sqrt(p'*(1-p')/n) =

1. Define the random variable X in words.

2. Define the random variable P′ in words.

3. Which distribution should you use for this problem?

4. Construct a 90% confidence interval, and state the confidence interval and the error bound.

5. What would happen to the confidence interval if the level of confidence were 95%?

Answer 1

Solution-:

Given:

1) Let, X= Number of voters answered for most significant issue was in the upcoming election is the economy
among 1200 voters.

2) p' = proportion of voters answered for most significant issue was in the upcoming election is the economy
among 1200 voters.

3) For this problem we use binomial distribution with parameter n is the number of trials and p is the probability of a success(i.e. voters answered )

When n is large and p is not close to zero or one, we can use the normal distribution to approximate the binomial.

4) The 90% C.I. for the population proportion is,

Where,

The error bound of proportion is,

5) The 95% C.I. for the population proportion is,

Where,

The width of 95 % C.I. is slighlty increses than 90% C.I.