Homework day 1 pg 92 94 for turn in day 2 pg 13 9 16

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Homework: Day 1: pg 568-70: 9.1, 9.2, 9.4 (for turn-in) Day 2: pg 578-80: 9.9-13, 9-16 (16d for turn-in)

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Chapter 9: Sampling Distributions Section 9.2: Sample Proportions Knowledge Objectives: Students will: Identify the “rule of thumb” that justifies the use of the recipe for the standard deviation of . Identify the conditions necessary to use a Normal approximation to the sampling distribution of . Construction Objectives: Students will be able to: Describe the sampling distribution of a sample proportion . (Remember: “describe” means tell about shape, center, and spread.) Compute the mean and standard deviation for the sampling distribution of . Use a Normal approximation to the sampling distribution of to solve probability problems involving . Vocabulary: Sample proportion – p-hat is x / n ; where x is the number of individuals in the sample with the specified characteristic (x can be thought of as the number of successes in n trials of a binomial experiment). The sample proportion is a statistic that estimates the population portion, p. Key Concepts: Conclusions regarding the distribution of the sample proportion: Shape: as the size of the sample, n, increases, the shape of the distribution of the sample proportion becomes approximately normal Center: the mean of the distribution of the sample proportion equals the population proportion, p. Spread: standard deviation of the distribution of the sample proportion decreases as the sample size, n, increases Sampling Distribution of p-hat For a simple random sample of size n such that n ≤ 0.10N (sample size is ≤ 10% of the population size) The shape of the sampling distribution of p-hat is approximately normal provided np ≥ 10 and n(1 – p) ≥ 10 The mean of the sampling distribution of p-hat is μ p-hat = p The standard deviation of the sampling distribution of p-hat is σ = √(p(1 – p)/n) Sample Proportions, p ̂ Remember to draw our normal curve and place the mean, p- hat and make note of the standard deviation Use normal cdf for less than values Use complement rule [1 – P(x<)] for greater than values
Chapter 9: Sampling Distributions Example 1: Assume that 80% of the people taking aerobics classes are female and a simple random sample of n = 100 students is taken. What is the probability that at most 75% of the sample students are female? Example 2: Assume that 80% of the people taking aerobics classes are female and a simple random sample of n = 100 students is taken. If the sample had exactly 90 female students, would that be unusual? Example 3: According to the National Center for Health Statistics, 15% of all Americans have hearing trouble. In a random sample of 120 Americans, what is the probability at least 18% have hearing trouble? Example 4: According to the National Center for Health Statistics, 15% of all Americans have hearing trouble. Would it be unusual if the sample above had exactly 10 having hearing trouble? Example 5: We can check for undercoverage or nonresponse by comparing the sample proportion to the population proportion. About 11% of American adults are black. The sample proportion in a national sample was 9.2%. Were blacks underrepresented in the survey?

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