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Lesson 8 - R

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.

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Lesson 8 - R

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  1. Lesson 8 - R Chapter 8 Review

  2. 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

  3. Vocabulary • None New

  4. Chapter 8 – Section 1 The sampling distribution of the sample mean is • The standard normal distribution with mean 0 and standard deviation 1 • The distribution of sample means • The histogram showing the relationship between the samples and the means • The method used to construct simple random samples

  5. 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 • Approximately normal • Very skewed right • Somewhat skewed left • Uniformly spread across its range

  6. 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 • 2 • 5 • 20 • 100

  7. Chapter 8 – Section 2 An example of a problem dealing with sample proportions is • Calculating the mean weight of elephants • Calculating the number of customers arriving at a bank between 1:00 pm and 1:10 pm • Calculating the ratio of people’s heights to their weights • Calculating the percent of cars that get more than 30 miles per gallon

  8. 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? • .33 / 500, or approximately .0007 • √.33•.67/500 , or approximately .021 • .33 • .66

  9. 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 • A standard deviation equal to • The sample proportion is approximately normal with • A mean equal to the population proportion • A standard deviation equal to

  10. 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

  11. 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 mina) P(x > 100) = 0.3875 normalcdf(100,E99,90,35)b) normal, μ = 90 min, σ = 35/10 = 11.068 minc) P(x-bar > 100) = 0.1831, no normalcdf(100,E99,90,11.068) • 11 p = 0.09 n = 200a) apx normal, μp=0.09, σp= (.09∙.91/200 = 0.0202b) 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 = $24.7487P(x > $400) = 0.5970 (not what we are looking for!)P(x-bar > $400) = 0.9588 normalcdf(400,E99,443,24.75)

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