1. Statistical Inference
Unit 6D
Statistical Inference
Ms. Young

2. Statistical Significance
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.
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.
Ms. Young

3. Margin of Error and Confidence Intervals
Suppose you draw a single sample of size n from a large population and measure its sample proportion.
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.
Discuss the relationship between the margin of error and the sample size.
Ms. Young

4. Margin of Error and Confidence Intervals
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% % + 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%.
Discuss the relationship between the margin of error and the sample size.
Ms. Young

5. null hypothesis: population parameter = claimed value
Hypothesis Testing
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.
Ms. Young

6. 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.
Ms. Young

7. Hypothesis Test Decisions
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
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
Ms. Young