Question

Stanley StatStudent is diligently working on a project for class. He has collected a random sample of data and calculates a 95% confidence interval for the proportion of all professional baseball players that are left-handed to be 25.42 % space plus-minus space 11.11 % . But now he is stuck. He doesn't know how to explain what this means. 1) Help Stanley out by writing a sentence to explain what the confidence interval he has calculated means in the context of the problem he is working on. 2) Stanley feels like his confidence interval is very wide. He wonders if it is possible to make the confidence interval more narrow. What would he have to do in order to calculate a more narrow confidence interval? (There are two ways to do this.) 3) Which of the two ways you suggested in #2 would be the better way for Stanley to narrow the confidence interval? Explain.

Answer 1

1) The 95% confidence interval for the proportion of all professional baseball players that are left-handed is given as: 25.42% 11.11%. This means that there is a 0.95 probability that the true population proportion of all professional baseball players that are left-handed would lie between 25.42% and 11.11%

b) The confidence interval for the proportion here is computed as:

From the above formula there are 2 ways to narrow the above confidence interval. These are:

• Either to increase the sample size n which would decrease the margin of error as could be seen in the above formula and therefore the interval would be narrower.
• Decrease the confidence interval: This would make the z value to be lower and therefore would again decrease the margin of error and thus narrow the confidence interval.

c) As we would want the confidence interval to be the same as 95% to be more confident about the population proportion, therefore the first way that is increasing the sample size n would be a better method to narrow the confidence interval here.