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AP Statistics Section 10.1 B CI for Population Mean When is Known

AP Statistics Section 10.1 B CI for Population Mean When is Known. The construction of a confidence interval for a population mean is appropriate when:. 1. the data comes from an SRS for the population of interest.

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AP Statistics Section 10.1 B CI for Population Mean When is Known

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  1. AP Statistics Section 10.1 BCI for Population Mean When is Known

  2. The construction of a confidence interval for a population mean is appropriate when:

  3. 1. the data comes from an SRSfor the population of interest.

  4. 2. the sampling distribution of is approximately Normal.

  5. 3. individual observations are independent.when sampling without replacement, the population size N is at least 10 times the sample size n.

  6. Example: Assume the distribution of is Normal. Find the z-scores that will capture the population mean in 88% of the SRSs. In other words, find the z-values that will produce an 88% confidence level.

  7. These z-scores that “mark off” a specified area under the Standard Normal curve are often called critical values. The z-score with probability p lying to its right under the standard Normal curve is called the __________________ and is denoted by ____

  8. The following confidence levels and their associated upper p critical values are so common that they are worth memorizing.

  9. When constructing a confidence interval you should use the tools from the Inference Toolbox.Step 1: _______________ Identify the population of interest and the parameter you want to draw the conclusions about.Step 2: _______________ Choose the appropriate inference procedure and verify the conditions for using it.Step 3: _______________ Carry out the inference procedure: confidence interval = estimate margin of errorStep 4: ___________________ Interpret your results in the context of the problem. Remember the three C’s: conclusion, connection andcontext.

  10. Example: A manufacturer of high-resolution video terminals must control the tension on the mesh of fine wires that lies behind the surface of the viewing screen. Too much tension will tear the mesh and too little will allow wrinkles. The tension is measured by an electrical device with output readings in millivolts (mV). Some variation is inherent in the production process. Careful study has shown that when the process is operating properly, the standard deviation of the tension readings is mV.

  11. Construct and interpret a 90% CI for the mean tension of all the screens produced on this day.

  12. Parameter: The population of interest isWe want to estimate , the high resolution terminals produced on a given day. mean tension for these screens.

  13. Conditions: Since we know ____ use the CI for a population mean where is known.SRS: Normality: Since we do not know if the population distribution is Normal….CLT?

  14. Boxplot Normal probability plot?

  15. Independence:

  16. Calculations:

  17. Interpretation:

  18. TI-83/84:

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