Warm-up 8.1 Estimating a proportion w/ confidence It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children. Can you apply the Central Limit Theorem to describe the sampling distribution model for the sample proportion of children who are nearsighted? Check the conditions and discuss any assumptions you need to make.

8.1 Estimating Proportion with Confidence The Pew Research Center found that 55%of singles ages 18–29 say that they aren’t in a committed relationship and are not actively looking for a romantic partner. This percentage is based on interviews with 1068 singles. The researchers are 95%confident. What, exactly, can they mean by this? The answer involves the concept of reasonably likely events.

How Confidence Intervals are used in relation to proportions Coral reefs are an integral part of marine life. Scientists say that 10% of the world’s reef systems have been destroyed in recent times. At current 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 Las Redes Reef in Akumal, Mexico. They found that 54 out of the 104 sea fans sampled were diseased. Find the confidence interval and list the strongest to weakest statements that can be made based on the given on the information above.

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 470 The 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 40 students to make the Vulcan salute with both hands at once. Count the number who are successful. 2.  Suppose you can reasonably consider your sample of 40 students a random sample of all students. From the data you gathered, is it plausible that 10% of all students could make this salute? Is it plausible that the true percentage is 60%? What percentages do you think are plausible?

Problem 2 using 1-PropZInt Problem 1: In January 2007 a Fox news poll of 900 registered voters found that 82% of the respondents believed global warming exists. Fox reported a confidence interval of 90% with a + 2% margin of error. 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

Homework 8.1 E # 7 – 10, 16 and 17 Read 8.2

Inference for Distributions Confidence Intervals Sample Proportion Sample Mean (known ) Sample Mean (unknown ) General formula Specific formula Expanded formula Calc Function 1-Prop Z Interval Z interval T Interval C 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 precise critical 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 our confidence 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?