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AP Statistics: Section 10.1 A

AP Statistics: Section 10.1 A. Statistical inference provides methods for drawing conclusions about a population from sample data. The two most common types of formal statistical inference are.

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AP Statistics: Section 10.1 A

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  1. AP Statistics: Section 10.1 A

  2. Statistical inference provides methods for drawing conclusions about a population from sample data. The two most common types of formal statistical inference are

  3. Sample values, such as a proportion or mean, will probably vary from sample to sample, but there is only one true population proportion or mean. Only by considering our sample as one of many such samples can we draw inferences.

  4. Inference is most reliable when the data is produced by a properly ____________ design.

  5. The sampling distribution of describes how the values of vary in repeated samples. Recall from Chapter 9 that the sampling distribution of will have the mean __ and a standard deviation _____.

  6. Furthermore, the Central Limit Theorem tells us

  7. Also recall, if the population is Normally distributed, then the distribution of will be Normally distributed regardless of our sample size.

  8. Example: The admissions director at Big City University proposes using the IQ scores of current students as a marketing tool. The university decides to provide him with enough money to administer IQ tests to an SRS of 50 of the university’s 5000 freshman. The mean IQ score for the sample is 112. What can the director say about the mean score of the population of all 5000 freshman?

  9. Now, 112 is probably not the true population mean for the IQ of Big City University freshman. The goal of a confidence interval is to give a range of values that we are “confident” the true population mean will lie within. The following will give us a glimpse of how this is done.

  10. When the distribution of is Normally distributed, the 68-95-99.7 rule for Normal distributions says that in about 95% of all samples, the mean score, , for the sample will be within ___ standard deviations of the population mean .

  11. So, whenever is within 2 standard deviations of , is within 2 standard deviations of . So the unknown lies between ________ and ________ in about 95% of all samples.

  12. For the example above, let’s assume the standard deviation of freshman IQ scores at BCU is 15, so the standard deviation of =

  13. So, we estimate that lies somewhere in the interval from =_______ to = _______. Our sample of 50 freshmen gave . The resulting interval is 112 4.2 or ( _____, _____ ).

  14. The key idea is that the sampling distribution of tells us how big the error is likely to be when we use to estimate .

  15. Understand that our confidence is in the procedure used to generate the interval.

  16. It is incorrect to try and associate any type of probability to an already found intervalbecause there are only two possibilities:

  17. 1. The interval between 107.8 and116.2 contains the true 2. Our SRS was one of the fewsamples for which is notwithin 4.2 points of the true . Only ____ of our samplesgive such inaccurate results.

  18. The interval of numbers is called a 95% _______________________for . It catches the unknown in 95% of all possible samples.

  19. The is called the

  20. The 95% is the

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