Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 7-1 Sampling Distribution - Sample Proportion
Transcript
SWBA T: Find the mean and standard deviation od the sampling distribution of a sample proportion Lesson 7-1 Do Now: A newspaper poll reported that 73% of respondents liked business tycoon Donald Trump. The number 73% is (a) a population (b) a parameter (c) a sample (d) a statistic (e) an unbiased estimator ACTIVITY: The candy machine 1. Launch the Reese’s Pieces® applet at w ww.rossmanchance.com. 2. C lick on the “Draw Samples” button. An animated simple random sample of n = 25 candies should be dispensed. Was your sample proportion of orange candies(look at the value of ̂ in the applet window) close to the actual population proportion, p = 0.5? 3. C lick “Draw Samples” 9 more times, so that you have a total of 10 sample results. Look at the dotplot of your ̂ values. What is the mean of your 10 sample proportions? What is their standard deviation? 4. To take many more samples quickly, enter 390 in the “num samples” box. C lick on the Animate box to turn the animation off. Then click “Draw Samples.” You have now taken a total of 400 samples of 25 candies from the machine. Describe the shape, center, and spread of the approximate sampling distribution of ̂ shown in the dotplot. SWBA T: Find the mean and standard deviation od the sampling distribution of a sample proportion Lesson 7-1 5. How would the sampling distribution of the sample proportion ̂ change if the machine dispensed n = 50 candies each time instead of 25? “Reset” the applet. Take 400 samples of 50 candies. Describe the shape, center, and spread of the approximate sampling distribution. 6. How would the sampling distribution of ̂ change if the proportion of orange candies in the machine was p = 0.15 instead of p = 0.50? Does your answer depend on whether n = 25 or n = 50? Use the applet to investigate these questions. Then write a brief summary of what you learned. Sampling distribution of p-hat – Mean and Standard Deviation Choose an SRS of size n from a population of size N with proportion p of successes. Let ̂ be the sample proportion of successes. Then: The M EAN of the sampling distribution of ̂ is = The S TANDARD DEVIATION of the sampling distribution of ̂ is (1 − ) = √ *As n increases, the sampling distribution of ̂ becomes approximately Normal. Before you perform Normal calculations, check that the Normal condition is satisfied: np > 10 and n(1-p) > 10. SWBA T: Find the mean and standard deviation od the sampling distribution of a sample proportion Lesson 7-1 Example: About 75% of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion ̂ in this sample who watch online video. (a) What is the mean of the sampling distribution of ̂ ? Explain. (b) Find the standard deviation of the sampling distribution of ̂ . C heck that the 10% condition is met. (c) Is the sampling distribution of ̂ approximately Normal? C heck that the Normal condition is met. (d) If the sample size were 9000 rather than 1000, how would this change the sampling distribution of ̂ ?
