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Sampling Distribution Models Part 1

Sampling Distribution Models Part 1. Sampling distributions of Proportions and Means C.L.T. The different models. The Normal Model ( BoB ) – The Probability Model (random variable E(X)) – Bernoulli trials, success failure ( p,q – 2 models) –.

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Sampling Distribution Models Part 1

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  1. Sampling Distribution ModelsPart 1 Sampling distributions of Proportions and Means C.L.T

  2. The different models The Normal Model (BoB) – The Probability Model (random variable E(X)) – Bernoulli trials, success failure (p,q – 2 models) –

  3. Sample Distribution of a Proportion ( ) Assumptions & Conditions: Independence Assumption a- Randomization Condition or b- 10% condition (less than 10% of population Sample Size Assumption – need large enough sample a- success/ failure condition np and nq both ≥ 10

  4. Sample Distribution of a Proportion ( ): Normal Model a- mean = b- stddev = *notice that we divided both binomial formulas by n to get the proportion formulas.

  5. Sample Distribution of a Mean ( ÿ ): • used with quantitative data. • Normal Model • a- mean = • b- stddev = • Sample Size Assumption – need large enough sample • a- success/ failure condition • np and nq both ≥ 10

  6. 37) Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. a) What percentage of pregnancies should last between 270 and 280 days?

  7. 37) Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. b) At least how many days should the longest 25% of all pregnancies last?

  8. 37) Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. c) Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. Let y-bar be the mean length of their pregnancies. According to the CLT, what’s the distribution of the sample mean, y-bar? Specify the model, mean and stddev.

  9. 37) Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. d) What’s the probability that the mean duration of these patients’ pregnancies will be less than 260 days?

  10. Change gears! Part 2

  11. Imagine:What would happen if we drew many random samples of the same size from the same population and considered the values for our sample statistic? Go to the N-spire activity

  12. Work on the N-spire activity

  13. When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailings list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100 and 200. For each sample size, they simulated 1000 mailings with success rate p = 0.05 and constructed the histogram of the 1000 sample proportions, shown below. Explain how these histograms demonstrate what the CLT says about the sampling distribution model for sample proportions. Be sure to talk about shape, center, and spread.

  14. 20 100 50 75

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