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Chapter 5

Chapter 5. Section 2 Part 2. Vocabulary Review. Population - entire group of people or items for which we are collecting data Sample – selections of the population that is used to make inferences about the population Parameter – a number or percentage that represents the population

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Chapter 5

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  1. Chapter 5 Section 2 Part 2

  2. Vocabulary Review • Population - entire group of people or items for which we are collecting data • Sample – selections of the population that is used to make inferences about the population • Parameter – a number or percentage that represents the population • Statistic – a number of percentage that represents the sample • Bias – A systematic error in measuring the estimate • favors certain outcomes • Sampling Variability – variability between different samples

  3. What do samples tell us? • We know that surveys can have variability, how do we take the variability and translate it into a statement of confidence? • The Margin of Error conveys how much confidence we have in the results of a survey by translating the sampling variability.

  4. What a margin of error means? • Given the following statement: • If we took many samples using the same method we used to get this one sample, 95% of the samples would give a result within plus or minus 3 percentage points of the truth about the population. • The margin of error is the plus or minus 3 percentage points • 95% of all samples came close to the truth, but 5% miss the mark by more than the margin of error. We don’t know the truth about the population, so we don’t know if our sample is one of the 95% that hit or one of the 5% that miss. We say we are 95% confident that truth lies within the margin of error.

  5. Method for Margin of Error • If you use the sample proportion p from a simple random sample of size n to estimate an unknown population proportion, p, then the margin of error for 95% confidence is roughly equal to 1 / • Actual Formula for 95% confidence interval • 1.96 ( )

  6. Example • In a survey of 705 people, 14% said that they watch television more than 12 hours per week. What is the margin of error? • The quick method reveals an important fact about how margins of error behave. Since the sample size n appears in the denominator of the fraction, larger samples have smaller margins of error.

  7. Working backwards • Given the margin of error….how many people were sampled • ± 5.5%

  8. Homework

  9. Confidence Statements • A Confidence Statement has two parts: a margin of error and a level of confidence. The margin of error says how close the sample statistics lies to the population parameter. The level of confidence says that percent of all possible samples satisfy the margin of error.

  10. Normal curve Formula for Confidence interval: Note: For confidence intervals, we DO NOT know p – so we MUST substitute p-hat for pin both the SD & when checking assumptions.

  11. A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

  12. We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.

  13. Standard Conclusion • We are 95% confident that the true proportion of ___________________ is between ______% and ______%.

  14. Important hints for interpreting confidence statements • The conclusion of a confidence statement always applies to the population, not the sample • Our conclusion about the population is never completely certain • A sample survey can choose to use a confidence level other than 95%. A higher confidence level means and larger margin of error • It is usual to report the margin of error for 95% confidence • Want a smaller margin of error with the same confidence? Take a larger sample

  15. Population size doesn’t matter • The variability of a statistics from a random sample does not depend on the size of the population, as long as the population is at least 10 times larger than the sample • 10 * n < Population

  16. Example

  17. Homework

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