Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work

Copyright © 2011 Pearson Education, Inc. Slide 6-3 Unit 6D Statistical Inference

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-4 Statistical Significance Common levels of significance: At the 0.05 level – The probability of an observed difference occurring by chance is 1 in 20 or less. At the 0.01 level – The probability of an observed difference occurring by chance is 1 in 100 or less. A set of measurements or observations in a statistical study is said to be statistically significant if it is unlikely to have occurred by chance.

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-5 The margin of error for 95% confidence is The 95% confidence interval is found by subtracting and adding the margin of error from the sample proportion. You can be 95% confident that the true population proportion lies within this interval. Suppose you draw a single sample of size n from a large population and measure its sample proportion. Margin of Error and Confidence Intervals

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-6 Example: A survey of 1200 people finds that 47% plan to vote for Smith for governor. Find the margin of error. Find the 95% confidence interval for the survey. 47% – 2.9% = 44.1% 47% + 2.9% = 49.9% We can be 95% confident that the true proportion of people who plan to vote for Smith is between 44.1% and 49.9%. Margin of Error and Confidence Intervals

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-7 The null hypothesis claims a specific value for a population parameter. It takes the form null hypothesis: population parameter = claimed value The alternative hypothesis is the claim that is accepted if the null hypothesis is rejected. Hypothesis Testing

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-8 Outcomes of a Hypothesis Test Rejecting the null hypothesis → We have evidence that supports the alternative hypothesis. Not rejecting the null hypothesis → We lack sufficient evidence to support the alternative hypothesis.

6-D Copyright © 2011 Pearson Education, Inc. Slide 6-9 less than 1 in 100 → strong evidence to reject the null hypothesis less than 1 in 20 → moderate evidence to reject the null hypothesis greater than 1 in 20 → not sufficient evidence to reject the null hypothesis Compare the actual sample result to the result expected if the null hypothesis is true. If the chance of a sample result at least as extreme as the observed result is Hypothesis Test Decisions