WARM – UP A local newspaper conducts a poll to predict the outcome of a hotly contested state ballot initiative that would legalize gambling. After conducting a random sample of 1200 voters, they find 624 support the initiative. What is the pop. support? a.) Define p and check the assumptions. b.) Construct and Interpret a 95% Confidence Interval. p = The true proportion of voters who support the initiative. SRS – Stated Appr. Norm: 1200(.52)=624 ≥ 10 1200(1 - .52)=576 ≥ 10 One Proportion Z– Conf. Int. We can be 95% confident that the true proportion of state voters who support the initiative is between 0.492 and 0.548.

What happens to the width of the Confidence interval if you… Increase your Confidence Level? 2. Increase your sample size? Interval gets wider Interval gets Narrower.

Choosing a Sample Size (Chapter 19 cont.) Margin of Error: Solve for n: (Divide both sides by z* and then square both sides.) (Invert.) (Multiply by p(1 – p). )

Choosing a Sample Size (Chapter 19 cont.) OR p* = The Conservative p = 0.5 unless otherwise noted.

ALWAYS ROUND UP!!! Sample is 4 times bigger. EXAMPLE 1: A local newspaper conducts a poll to predict the outcome of a hotly contested state ballot initiative that would legalize gambling. Previous polling has revealed at of 55%. At least what sample size must be collected in order to estimate the proportion within 4% points with 90% Confidence? ALWAYS ROUND UP!!! What happens to the sample if you cut the margin of error in half? Sample is 4 times bigger.

Since no p was given, use the conservative p* = .5 EXAMPLE 2: A company wants to estimate the true proportion of consumers that may buy the company’s newest product. At least what sample size must be collected in order to estimate this proportion within 5% points with 95% Confidence? Since no p was given, use the conservative p* = .5

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