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AP Statistics Section 11.1 B More on Significance Tests

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## AP Statistics Section 11.1 B More on Significance Tests

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**Conditions for Significance TestsThe three conditions that**should be satisfied before we conduct a hypothesis test about an unknown population mean or proportion are the same as they were for confidence intervals: 1. _______ from the population of interest.2. Distribution of must be ________________ For : _________________________________ For : ________________________3. _________________________ If sampling w/o replacement ___________**Example 1: Check that the conditions from the paramedic**example in section 11.1 A are met.SRS:Normality of :Independence:**Test StatisticsA significance test uses data in the form of**a test statistic. The following principles apply to most tests: (1) the test statistic compares the value of the parameter as stated in the __ to an estimate of the parameter from the sample data. (2) values of the estimate far from the parameter value in the direction specified by the alternativehypothesis give evidence _____________ (3) to assess how far the estimate is from the parameter, standardize the estimate.**In many common situations, the test statistic has the**form:test statistic = -----------------------------------------**Because the result is over two standard deviations below the**hypothesized mean 6.7, it gives good evidence that the mean RT this year is not equal to 6.7 minutes, but rather, less than 6.7 minutes.**The probability, computed assuming __________, that the**observed sample outcome would take a value as extreme as or more extreme than that actually observed is called the __________ of the test.**The smallerthe P-value is, the strongerthe evidence is**against provided by the data.**Example 3: Let’s go back to our paramedic example. The**P-value is the probability of getting a sample result at least as extreme as the one we did ( = 6.48) if were true. In other words, the P-value is calculated assuming . We just found the z-score for this exact situation, so using Table A or our calculator, this P-value is _______. So ifis true, and the mean RT this year is still 6.7 minutes, there is about a _____ chance that the city manager would obtain a sample of 400 calls with a mean RT of 6.48 minutes or less. The small P-value provides strong evidence against and in favor of the alternative minutes.**If the Ha is two-sided, both directions count when figuring**the P-value.**Example 4: Suppose we know that differences in job**satisfaction scores in Example 3 of section 11.1 A follow a Normal distribution with standard deviation . If there is no difference in job satisfaction between the two work environments, the mean is _______. Thus H0: ________. The Ha says simply “there is a difference,” thus Ha:________. Data from 18 workers gave 17. That is, these workers preferred the self-paced environment on average. Find the p-value for this situation and interpret it.**A p-value of .2302 indicates that 23.02% of the time we will**get a sample where is at least as big as 17 when . An outcome that would occur this often when is not good evidence that .**Statistical SignificanceWe can compare the P-value with a**fixed value that we regard as decisive. This amounts to announcing in advance how much evidence against we will insist on. The decisive value of P is called the significance level. We write it as ____, the Greek letter alpha. If the P-value , we say that the data are**Example 5: Back to the paramedic example. We found the P =**0.0139. The result is statistically significant at the .05 level since P < ____ but it is not significant at the .01 level since P > ____“Significant” in the statistical sense does not mean “_____________.” It means simply “not likely to happen just by _________.”**Interpreting Results in ContextThe final step in performing**a significance test is to draw a conclusion about the competing claims you were testing. As with confidence intervals, your conclusion should have a clear connection to your calculations and should be stated in the context of the problem. These are called the 3C’s.**In significance testing, there are two accepted methods for**drawing conclusions:**In examples 3 and 4 of this section we simply stated the**p-value and interpreted it in the context of the problem.**In example 5, we went on to determine if the data was**statistically significant be comparing our P-value to our significance level . We can either _______ or _______________ the Ho based on whether our result is statistically significant at a given significance level.**Warning: if you are going to draw a conclusion based on**statistical significance, then the significance level should be stated before the data are produced.**Example 6: For the paramedic example, we calculated the**P-value to be 0.0139. If we were using an significance level, we would _____ minutes ( ________ ) since ______ ( __________ ). It appears that the mean response time to all life-threatening calls this year is less than last year’s average of 6.7 minutes ( ______ ).**Finally, stating a P-value is more informative than simply**giving a “reject” or “fail to reject” conclusion at a given significance level. For example, a P-value of 0.0139 allows us to reject at the level. But the P-value, 0.0139 gives us a better sense of how strong the evidence against is. The P-value is the smallest level at which the data are significant.