Review+Practice Contd.

Transcription

1 Review+Practice Contd. Mar 9, 2012 Final: Tuesday Mar 13 8:30-10:20 Venue: Sections AC and AD (SMITH 211 ), all other sections (GWN 301) Format: Multiple choice, True/False. Bring: calculator, BRAINS, STUDENT ID. (No scantron or blue book needed) Will be provided formula sheet, normal tables. Chance Probability Models: Definition A describes how we assign probabilities to a collection of outcomes. (choose all that apply) Probability model Histogram Sample Sampling distribution Someone wonders why the probability of rain isn t always 50% since there are only two outcomes (rain or no rain). Circle the best answer. Probabilities do not depend on the number of outcomes, rather their long-run frequencies. There are more than two outcomes since rain can be sub-classified into hail, snow and sleet. Rain obeys the laws of science, not the laws of chance.

2 Chance Probability Models: Derivation On a multiple-choice test, a student has four possible choices for each question, one of which is correct and the remaining 3 are incorrect. The student receives 1 point for a correct answer and loses 1 point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses at random, what is P(choosing correctly) and P(choosing incorrectly)? P(correct) = 0.25; P(incorrect) = 0.75 P(correct) = 0.75; P(incorrect) = 0.25 P(correct) = 0.5; P(incorrect) = 0.5 True or False: This probability model can also be written as draws made at random (with replacement) from a box. If true, give the contents of the box and if false explain your reasoning. Chance Probability Rules Which is not a probability rule? Any probability is a number between 0 and 100 All possible outcomes together must have a probability of 1 The probability that an event does not occur is 1 minus the probability that the event does occur. If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities

3 Chance Using Probability Rules If you draw a chocolate truffle from a bag of chocolates, the one you draw will have one of five flavors. The probability of drawing each truffle depends on the proportion of each flavor among all flavors made. Here are the probabilities of each flavor for a randomly chosen bag of chocolates: Flavor Probability Raspberry 0.25 Dark Chocolate 0.3 Mint 0.2 Peanut Butter 0.15 White Chocolate? What is the P(white chocolate)? None of the above P(not raspberry)? P(dark chocolate or mint)? P(orange)? Chance Sampling Distribution of p-hat Shown below are sampling distributions for p-hat based on S.R.S.s of size 100, 400 and 900 draws made from a population. Write the number of draws on which each sampling distribution is based in the blank provided below it.

4 Chance Using the Sampling Distribution of p-hat An opinion poll asks an S.R.S of 1000 adults Do you watch American Idol? Suppose the proportion of the population that watches American Idol is p=0.35. In a large number of samples, the proportion who answer that they watch American Idol will be approximately normally distributed with a mean of 0.35 and a standard deviation of What percentage of samples will have a sample proportion who watch American Idol between 0.25 and 0.45? 35% 50% 68% 100% Expected Values Definition The expected value of a random phenomenon with numerical outcomes is: The long-run average of the random phenomenon. Sum of the products of numerical outcomes and their respective probabilities. Both of the above None of the above

5 Expected Values Calculating from a Probability Model On a multiple choice test, a student has four possible choices for each question, one of which is correct and the remaining 3 are incorrect. The student receives 1 point for a correct answer and loses 1 point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses, what is their expected score on the question? None of the above Expected Values Long run Behavior of Averages A bored statistician begins to flip a coin. She flips the coin 5 times and records the proportion of heads. Then she flips the coin 15 times and records the proportion of heads. Then she flips the coin 30 times and records the proportion of heads. She begins to see a trend, the more times she flips the coin, the closer she gets to 0.5 heads. This is an example of: (choose all that apply) Confidence intervals Law of large numbers Sampling distribution Probability

6 Standard Errors Short run Behavior of Averages: Standard Error On a multiple choice test, a student has four possible choices for each question, one of which is correct and the remaining 3 are incorrect. Suppose he answers 10 questions in this manner. How close will his average score come to its expected value? ± 0.27 ± 0 ± 1 Statistical Inference Calculating 95% Confidence Intervals A newspaper poll on state budgetary issues interviewed 828 state residents. Of the residents surveyed, 470 of them felt that the state should balance the budget. Use the poll results to give a 95% confidence interval for p to to.6020 The Elway poll of 408 voters found that 64% of the sample favored a sales tax hike. The associated margin of error was ± 5 percentage points. A 95% confidence interval for the true proportion of Washingtonians who favor the hike is: 64% 59% - 69% 59% - 64%

7 Statistical Inference Interpreting Confidence Intervals A confidence interval: Tells us how uncertain the estimate is. Gives us a range of plausible values for the parameter. Helps to answer the question, How good is the statistic as an estimate of the parameter? All of the above. None of the above. Know what 95% confidence level means. Statistical Inference Tests of Significance A assesses the evidence for some claim about the value of an unknown parameter. Margin of error Confidence interval Test of significance None of the above Know the meanings of the null hypothesis, alternative hypothesis, statistically significant, P-value.

8 Statistical Inference Tests of Significance The N.Y. Times and C.B.S. News conducted a nationwide poll of 1048 randomly selected 13 to 17 year olds. Of these teenagers, 692 had a television in their room. They wish to conduct a test of significance to see if there is good evidence that more than half of all teenagers have a T.V. in their room. What is the null? What is the alternative? What is the statistic? What is the sampling distribution of the statistic under the null? What is the standard score? What is the P-value? What is your conclusion?