One-Sample Inference for Proportions

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Presentation transcript:

One-Sample Inference for Proportions AP Statistics Chapter 12

Introduction The statistic that estimates the parameter p is the sample proportion .

Confidence Interval for Proportions Assumptions: SRS The population has to be at least 10 times the sample size.

Formula for Confidence Interval

Example A die is rolled 25 times and 12 evens are observed. Create a 90% confidence interval to estimate the true proportion of evens rolled on a die.

Example Continued Assumptions - SRS assumed - population of all rolls is at least 10 times sample size. - Normality approximated for the sampling distribution by 25(.48)≥10 (12≥10)and 25(.52)≥10 (13≥10)

Example Continued We are 90% confident that the true proportion of evens obtained from rolling a die is in the interval from .3157 to .6444. Since random sample was assumed the results may not be valid.

Example for Hypothesis Test Test Statistic: Po is the assumed population parameter. It comes from the Ho statement.

Example Continued A study is performed investigating the fairness of dice. A die is rolled 75 times. 25 of the results yield an even number. Conduct a hypothesis test at a .05 level to see if the die is fair.

Example Continued Assumptions: SRS is assumed. The population of all rolls is at least 10 times the sample size. Both exceed 10, so normality is approximated for the sampling distribution. (Note that we don’t use the sample estimate as we did for confidence intervals.)

Example Continued Results for a one-proportion z-test: We will be using a 1Prop Z Test in Calculator.

Example Continued Conclusion: Since p(.0039) < α (.05), the results are significant and we reject Ho. We have sufficient evidence to believe that the true proportion of evens is not equal to .5. The die may not be fair. Since random sample assumed the results may not be valid.

Homework Worksheet #1-4 Bookwork 12.1-12.5 odds