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Understanding Plus Four: A Stability Guide for Confidence Intervals

This guide explores the significance of the Plus Four method, particularly its effectiveness in generating stable confidence intervals. While Plus Four is recommended for calculating confidence intervals, it is advised not to use it for hypothesis testing. The agenda covers various statistical topics, including population mean tests, comparisons of means, F-tests for equal variances, and Chi-square independence tests. Additionally, it offers preparation strategies for Midterm II, highlighting essential elements like hypothesis notation and estimating confidence interval bounds to enhance testing efficacy.

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Understanding Plus Four: A Stability Guide for Confidence Intervals

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  1. STAT 104 Section 9 Daniel Moon

  2. Why Plus Four? SEp of plus four are more stable! Plus four works for confidence interval But for hypothesis testing, don’t use plus four

  3. Agenda • Tests of Population mean μX • Comparisons of two means • F-test for equal variances • Chi-square independence test • Prep for Midterm II • Go over Practice Exam

  4. Tests of Population mean μX <Alan> • Has the average price of homes increased since the 2000 census reported mean and SD figures? • A survey in India showed birthweights had an average of 111 and SD of 16 ounces • The national Latin Achievement test has a mean of 600 and SD of 50; Do students from Boston Latin School score above the national average on this test?

  5. Agenda • Tests of Population mean μX • Comparisons of two means • F-test for equal variances • Chi-square independence test • Prep for Midterm II

  6. Comparisons of two means <Alan> • To determine if the length of commercials on public television increased in the past 10 years, tapes of some programs in 1996 and 2006 were analyzed • Surveys were conducted to determine if adults from MA are saving more or less than those from NY • Were airlines justified last month when they raised ticket prices due to an increase in passenger weight?

  7. Agenda • Tests of Population mean μX • Comparisons of two means • F-test for equal variances • Chi-square independence test • Prep for Midterm II

  8. F-test for equal variances • Test statistics F = larger s^2 / smaller s^2 • When you calculate p-value, • Don’t forget to multiply by 2 if it’s two-tail. <Alan>

  9. Agenda • Tests of Population mean μX • Comparisons of two means • F-test for equal variances • Chi-square independence test • Prep for Midterm II

  10. Chi-square independence test <Alan> • A survey was conducted to determine if the poverty rate for 1st generation immigrants from Brazil is the same in northern and southern states

  11. Agenda • Tests of Population mean μX • Comparisons of two means • F-test for equal variances • Chi-square independence test • Prep for Midterm II

  12. Prep for Midterm II • Write down your notation clearly, your hypotheses, your bounds for condence intervals, your rejection region, your estimates, your bounds for condence intervals, your rejection region, your estimates for sample statistics • Draw an approximate normal curve if you can to test yourself and make sure you are taking the right numbers (interior, tails, etc) from the table. Adequate chi2, F, t, Z tables will be provided, but you will often have to approximate. • Stating reasons for your choices is the best way to get credit. Yes there will be questionable moments as to which test/tails to use (as there are in real life!).

  13. Prep for Midterm II

  14. Tees (2007 Spring Midterm II. #2) • Stinger tees > Regular tees

  15. TV (2007 Spring Midterm II. #2) • Sufficient evidence to show that the time men now spend watching sports on TV is different from that in 1990?

  16. Hepatitis (2007 Spring Midterm II. #4) Determine if the risk of Hepatitis C was related to whether people had a tattoo? Relative risk of hepatitis C associated with having a tattoo

  17. Hepatitis (2007 Spring Midterm II. #5) • 2000 US census • # of people per household • Average: 2.5 , s.d. = 2 • Concern that this average has continued to drop since 2000.

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