SOLUTION: 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 profes

Question 1037564: 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 by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
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We are 95% confident that the population proportion is
between 25.42%-11.11% and 25.42%+11.11%
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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.)
Width depends on the Margin of error which is z*sqrt(p*q/n)
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Increasing "n" (the sample size) will shink the ME and therefore shink the width.
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Decrease ME by decreasing z by increasing the level of confidence.
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3) Which of the two ways you suggested in #2 would be the better way for Stanley to narrow the confidence interval?
Explain::: Increase the sample size.
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Cheers,
Stan H.
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