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Notes

Notes. We need to adapt our work with test of significance to deal with means not just proportions We continue to use our initial test of conditions Random Normal: ( np , n(1-p)) assuming p from Null Hypothesis Independent We’ll draw liberally from our work from last chapter.

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Notes

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  1. Notes • We need to adapt our work with test of significance to deal with means not just proportions • We continue to use our initial test of conditions • Random • Normal: (np, n(1-p)) assuming p from Null Hypothesis • Independent • We’ll draw liberally from our work from last chapter

  2. Definition, Revisited • Test Statistic • Measures how far a sample statistic diverges from what we should expect if the null hypothesis Ho is true, in standard units (similar to Z-score) • High values of this statistic give evidence against Ho • Because we’re talking about a mean as opposed to a parameter we must use the sample standard deviation to find the standard error. This causes us to use the t-distribution • Degrees of Freedom is used to find P (remember if using the Table be conservative with your estimate i.e. don’t inflate t)

  3. One Sample Z test of a average Check your understanding on page 574 • State the Null and Alternative Hypothesis • Check conditions • Calculate the Test Statistic • Find and interpret the P-Value

  4. Example of page 574 • State the Null and Alternative Hypothesis • Check conditions • Calculate the Test Statistic • Find and interpret the P-Value

  5. Example A student group claims that first-year students at a university study 2.5 hours per night during the school week. A skeptic suspects that they study less than that on average. He takes a random sample of 30 first-year students and finds that x-bar=137 minutes with a sx=45 minutes. A graph of the data shows no outliers but some skewness. Carry out an appropriate significance test at the 5% significance level. What conclusion do you draw?

  6. Definition • Paired Data (paired t procedure) • Analysis of data by looking at the difference between two data sets • Based on matched pairings

  7. Example For their second semester project in AP Statistics, Libby and Kathryn decided to investigate which line was faster in the supermarket: the express lane or the regular lane. To collect their data, they randomly selected 15 times during a week, went to the same store, and bought the same item. However, one of them used the express lane and the other used the regular lane. To decided which lane each of them would use, they flipped a coin. They entered randomly assigned lanes at the same time, and each recorded the time in seconds it took them to complete the transaction.Do they have convincing evidence as to which lane is faster?

  8. Notes • Notes on paired data • The data itself doesn’t need to be normal, just the difference • The same goes for independence • As with previous examples, a Confidence Interval will often give a more complete picture of the data • Note at the bottom of page 582 • Example of page 583—Not rejected the null is important as well • Always Remember: These formulas work for bad data. A poorly designed experiment or study can still be analyzed for significance. This doesn’t mean these assertions are valid even though the mathematics may be sound…

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