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Lesson 8 - R Chapter 8 Review Objectives • Summarize the chapter • Define the vocabulary used • Complete all objectives • Successfully answer any of the review exercises • Use the technology to compute means, standard deviations and probabilities of Sampling Distributions Vocabulary • None New Chapter 8 – Section 1 The sampling distribution of the sample mean is 1) The standard normal distribution with mean 0 and standard deviation 1 2) The distribution of sample means 3) The histogram showing the relationship between the samples and the means 4) The method used to construct simple random samples Chapter 8 – Section 1 If a random variable X has a skewed right distribution, then the distribution of the sample mean for a sample of size n = 500 for X is 1) 2) 3) 4) Approximately normal Very skewed right Somewhat skewed left Uniformly spread across its range Chapter 8 – Section 1 If a random variable X has a standard deviation σ = 20, then the standard error of the mean for a sample of size n = 100 is 1) 2) 3) 4) 2 5 20 100 Chapter 8 – Section 2 An example of a problem dealing with sample proportions is 1) Calculating the mean weight of elephants 2) Calculating the number of customers arriving at a bank between 1:00 pm and 1:10 pm 3) Calculating the ratio of people’s heights to their weights 4) Calculating the percent of cars that get more than 30 miles per gallon Chapter 8 – Section 2 A study found that 33% of adult females dye their hair. In a sample of 500 adult females, what proportion do we expect to find who dye their hair? 1) 2) 3) 4) .33 / 500, or approximately .0007 √.33•.67/500 , or approximately .021 .33 .66 Chapter 8 Summary • The sample mean and the sample proportion can be considered as random variables • The sample mean is approximately normal with – A mean equal to the population mean x – A standard deviation equal to x / n • The sample proportion is approximately normal with p̂ p – A mean equal to the population proportion – A standard deviation equal to p̂ p( 1 p ) / n Summary and Homework • Summary – Samples of sample means have the same means as population, but have tighter spreads (less variance) than the population – Samples of sample proportions have the same proportion as the population, but also have less variance than the population • Homework: – pg 443 – 444; 4, 6, 11, 14 Homework • 4: sampling distro of x-bar: mean: μ stdev: σ/n sampling distro of p-hat: mean: p stdev: (p)(1-p)/n • 6 μ=90 min σ=35 min a) P(x > 100) = 0.3875 normalcdf(100,E99,90,35) b) normal, μ = 90 min, σ = 35/10 = 11.068 min c) P(x-bar > 100) = 0.1831, no normalcdf(100,E99,90,11.068) • 11 p = 0.09 n = 200 a) apx normal, μp=0.09, σp= (.09∙.91/200 = 0.0202 b) P(p-hat ≤ 0.06) = 0.0688 normalcdf(-E99,0.06,0.09,0.0202) c) P(x ≥ 25) = 0.0416, Yes normalcdf(0.125,E99,0.09,0.0202) • 14 μ=$443 σ=$175 n=50 σx-bar = $175/50 = $24.7487 P(x > $400) = 0.5970 (not what we are looking for!) P(x-bar > $400) = 0.9588 normalcdf(400,E99,443,24.75)