AP Statistics – Chapter 9 Test Review I can interpret P-values in context. • QUESTION: When we are testing hypotheses, what would be strong evidence against the null hypothesis ( )? • ANSWER: Obtaining data that shows a very small p-value. (in comparison to the stated ‘alpha’ level … which is usually going to be 0.05) I can interpret a Type I error and a Type II error in context, and give the consequences of each. • A Type I Error is: – When we REJECT the null hypothesis, when the null hypothesis, is in fact TRUE. • A Type II Error is: – When we FAIL TO REJECT the null hypothesis, when the null hypothesis is in fact FALSE. I can understand the relationship between the significance level of a test, P(Type II error), and power. • The probability of committing a TYPE I ERROR is: – Whatever, your value for α is (your significance level, whatever it is stated to be; DEFAULT level = 0.05 (5%)) • The probability of committing a TYPE II ERROR is: –β I can interpret a Type I error and a Type II error in context, and give the consequences of each. • What is POWER? – It is your ability to correctly identify a FALSE null hypothesis (Ho). (probability of correctly rejecting a FALSE null hypothesis) • What are some ways to INCREASE the power of a test? – Increase sample size ‘n’…. While keeping significance level the same… – Increase significance level α…. Which also means increasing the risk of making a Type I Error… I can check conditions for carrying out a test about a population proportion. • What are the assumptions for 1 prop z test – RANDOM? • Sample must be random…. • No VRS’s or Convenience samples – NORMAL? • Confidence Intervals: – ∗ ≥ 10; ∗ ≥ 10 • Significance Tests: – ∗ ≥ 10; ∗ ≥ 10 – INDEPENDENT? • AKA: 10% Rule – “We are sampling without replacement…. So population must be 10 times larger than the sample.” I can check conditions for carrying out a test about a population mean. • What are the assumptions for 1 sample t test – RANDOM? • Same for 1 prop z test – NORMAL? • We must consider the sample size and whether it is large enough. We prefer it to be greater than 30. This is especially important if we don’t know if the POPULATION is NORMAL or not. The Central Limit Theorem is what allows us to assume normality AS LONG AS THE SAMPLE SIZE IS GREATER THAN 30… • Additionally, if the sample size is LESS THAN 30, we must look at the data graphically and determine if there is strong skew ness or the presence of outliers, which can cause us to doubt the normality of the data. – INDEPENDENT? • Same for 1 prop z test I can describe the sampling distribution for proportions or means. • When we describe a sampling distribution, we must ALWAYS address THREE things: – CENTER • This is either ‘p’ or ‘μ’. Whatever they say these values are, are to be the values you use to describe the CENTER. (Note: in most instances, we call the center “Mean”, whether it is a proportion or not.) • Do NOT us the p-hat or x-bar (statistics) values in place of the parameter values…!!!! – SPREAD • This is standard deviation. – Proportions: – Means: – SHAPE • If the sample size is GREATER than 30, then we can say it is ‘approximately normal.’ • If the sample size is LESS than 30, we can only say its ‘approximately normal’ as long as there are no outliers or strong skew ness in the sample data. I can check conditions for carrying out a test about a population mean OR proportion. • Suppose, you are testing the NORMAL condition for a test of either MEANS or PROPORTIONS. If your sample data, had a box plot, that looked like this, how would you react? • If the sample size was 100? – It would be safe to assume normality (n > 30) • If the sample size was 22? – It would NOT safe to assume normality because…. (n < 30) I can recognize when a confidence interval is not needed for estimations. • QUESTION: If you are able to obtain data from a population through a CENSUS, rather than through a SAMPLE, when would it be appropriate to make estimations via CONFIDENCE INTERVALS or decisions via SIGNIFICANCE TESTING? – ANSWER: • NEVER… if you have 100% of the data from the ENTIRE population, then what are you estimating or trying to decide???? (i.e.: You already know the PARAMETER values… so, don’t bother with carrying out a test or constructing an interval). I can recognize paired data and use one-sample t procedures to perform significance tests for such data. • When we are doing a hypothesis test for PAIRED DATA… – What type of Test do we do for paired data and what is the parameter of interest? • TYPE OF TEST: 1 sample t-test • PARAMETER OF INTEREST: The mean difference μ – What will the null hypothesis look like? • MEANS: : = I can interpret P-values in context. • Suppose I obtain a p-value that is 0.068 • Is this significant at? – 10% level (0.10)? • YES – 5% level (0.05)? • NO – 1% level (0.01)? • NO Test will consist of: • 16 Multiple Choice Questions • 2 Free Response Question – Some students will get a 1 PROP Z-TEST, others will get a 1 SAMPLE T TEST BASELINE TOPIC(S): • Must get AT LEAST ¾ on the FRQ • MULTIPLE CHOICE TOPIC(s): – MUST know how to calculate DEGREES OF FREEDOM in order to find a ‘t’ test statistic – MUST know the definition of Type II Error – MUST know how to read a situation and correctly state the NULL & ALTERNATIVE hypotheses for a mean or a proportion.