Warm-up8.1 Estimating a proportion w/ confidence

It is generally believed that nearsightedness affects about12% of all children. A school district has registered 170incoming kindergarten children.a) Can you apply the Central Limit Theorem to describe thesampling distribution model for the sample proportion ofchildren who are nearsighted? Check the conditions anddiscuss any assumptions you need to make.

8.1 Estimating Proportion with ConfidenceThe Pew Research Center found that 55%of singles ages18–29 say that they aren’t in a committed relationship andare not actively looking for a romantic partner. Thispercentage is based on interviews with 1068 singles. Theresearchers are 95%confident. What, exactly, can theymean by this? The answer involves the concept ofreasonably likely events.

How Confidence Intervals are used in relation to proportionsCoral reefs are an integral part of marine life. Scientists say that 10%of the world’s reef systems have been destroyed in recent times. Atcurrent rates of loss, 70% of the reefs could be gone in 40 years.Scientists sampled a specific kind of coral called a sea fan out of LasRedes Reef in Akumal, Mexico. They found that 54 out of the 104 seafans sampled were diseased. Find the confidence interval and list the strongest to weakeststatements that can be made based on the given on the informationabove.

Rank the following statements

1. 51.9% of all sea fans on the Las Redes Reef are infected.2. It is probably true that 51.9% of all se fans on the Las Redes Reef

are infected.3. We don’t know exactly what proportion of sea fans on the Las

Redes Reef is infected but we know that it’s within the interval of 51.9% + 4.9%. That is, it’s between 42.1% and 61.7%

4. We don’t know exactly what proportion of sea fans on Las Redes Reef is infected, but the interval from 42.1% to 61.7% probably contains the true proportion._____ , ______ , _____ , _____

Strongest … to … Weakest

Can you come up with a better statement?

Vulcan Salute pg 470The Vulcan salute from Star Trek, which means “live long and prosper,” originated as part of a blessing in Jewish ceremony. Your goal is to estimate what proportion of students can make this salute, clearly and easily, with both hands.• Without giving anyone the chance to practice, ask exactly 40students to make the Vulcan salute with both hands at once. Count thenumber who are successful.2. Suppose you can reasonably consider your sample of 40 students arandom sample of all students. From the data you gathered, is itplausible that 10% of all students could make this salute? Is it plausiblethat the true percentage is 60%? What percentages do you think areplausible?

Problem 2 using 1-PropZIntProblem 1: In January 2007 a Fox news poll of 900 registeredvoters found that 82% of the respondents believed globalwarming exists. Fox reported a confidence interval of 90% witha + 2% margin of error.

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This confidence interval is reasonably accurate when three conditions are met: 1) The sample was a simple random sample from a binomial population. 2) Both np and n(1 − p ) are at least 10. ‘3)The size of the population is at least 10 times the size of the sample

Homework1) 8.1 E # 7 – 10, 16 and 172) Read 8.2

Inference for Distributions

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Confidence Intervals

8.2 Testing a Proportion 9.1 Confidence Interval of the Mean 9.2 Significance Testing for the Mean

8.1 (Day 2) Confidence Intervals and Margin of Error

So far we have learned that a 95% confidence interval has a precisecritical value of z* = 1.96 and to find the confidence interval we used

Z* , the critical value, can change based on the size we want ourconfidence interval to be.

This process is also called a one-proportion z-interval .

What will be the z*, critical value, for a 90% confidence interval?

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