Midterm Study Sheet for Statistics: Key Concepts and Confidence Intervals, Exams of Statistics

Download Midterm Study Sheet for Statistics: Key Concepts and Confidence Intervals and more Exams Statistics in PDF only on Docsity! 11/10/2006 STUDY SHEET for MIDTERM #3 (Friday, November 17) - Ch. 6 (section 6.6) - Ch. 7 (skip 7.5) - Ch. 8 (skip 8.6) - Ch. 9 (9.2, 9.4) The best way to prepare to the midterm is to read the book and to do the homework exercises. Please, take time to go over the material. Here is what you have to have an idea about: 1. Normal distribution as approximation to Binomial distribution: conditions, continuity correction. 2. A point estimate. Interval estimates. Confidence level. Confidence intervals. 3. Confidence intervals for means (large samples). Maximum error of estimate. 4. Minimum sample size needed for an interval estimate of the population mean. 5. Confidence intervals for means (small samples). t-distribution. Degrees of freedom. 6. Confidence intervals for proportions. Maximum error of estimate. 7. Sample size determination for estimating proportion. 8. A statistical hypothesis, Null hypothesis, Alternative hypothesis, Type I error, Type II error. 9. Components of a traditional hypothesis test. Two-tailed alternative, one-tailed alternative. Level of significance. Critical values. Test Statistics. 10. Test concerning mean (large sample). 11. P-value method. 12. Test concerning mean (small sample). 13. Test concerning proportion. 14. Testing the difference between two means (large samples). 15. Testing the difference between two means (small samples). Below is the most general formulation of typical problems which you can expect on the test: 1. Given a Binomial distribution problem, use Normal approximation to find the answer. Do not forget to check conditions and apply continuity correction. {6.6} 2. Given a degree of confidence, find the corresponding critical values for construction of confidence interval. {7.2} 3. Given a sample size ( ), the degree of confidence and the standard deviation, calculate the margin of error for the mean estimate. {6.2} 30≥n 4. Given a sample size ( ), the degree of confidence, the sample mean and the population (or sample) standard deviation, construct the confidence interval for the population mean. {7.2} 30≥n 5. Given the maximum error estimate, the degree of confidence and either the population or sample standard deviation, find the sample size. {7.2} 6. Given the sample size (n < 30), the degree of confidence, the sample mean and the sample standard deviation, construct the confidence interval for the population mean. Use t-distribution to find critical values.{7.3} 7. Calculate the maximum error of the estimate of a population proportion. Given the sample size, the degree of confidence and the sample proportion, construct the confidence interval for the actual population proportion. {7.4} 8. Given the maximum error, the degree of confidence and the estimate for population proportion, find the sample size. Given the maximum of error and the degree of confidence but without knowledge of the estimate for population proportion, find the sample size. {7.4} 9. For a given problem, formulate the null and alternative hypotheses. Find the errors (in words) of the I and II types. {8.2} 10. For a given problem, identify the parameter of interest. Formulate a null hypothesis and an appropriate alternative hypothesis in terms of the parameter of interest. Identify whether you have two-tailed or one-tailed test. Based on the choice of the level of significance, find the critical values and identify the critical region. Calculate from the sample data the value of the test statistic on which the decision is to be based. Make a decision. {8.3, 8.4, 8.5, 9.2, 9.4} 11. Given the test statistics, find the corresponding p-value and make decision about null hypothesis based on this p-value and the level of significance. {8.3, 8.4, 8.5, 9.2, 9.4} True-false questions: 1. If we increase the confidence level, then we decrease the width of the confidence interval. 2. In a significance test, if there is not enough evidence to reject the null hypothesis, we accept it. 3. The test value separates the rejection region from nonrejection region. 4. Increasing the sample size increases the probability of making a Type I error.