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Confidence Intervals and Hypothesis Tests
Confidence Intervals and Hypothesis Tests
Statistical inference uses sample data to make statements about a population.
Confidence Interval
A confidence interval gives a plausible range for a population parameter.
General Form
Estimate $\pm$ margin of error.
Hypothesis Test
Start with a null hypothesis $H_0$ and an alternative $H_a$. The p-value measures how surprising the data are if $H_0$ were true.
Interpretation
A small p-value is evidence against the null hypothesis. It is not the probability that the null is true.
Example 1
A 95% confidence interval for a mean is $(48,52)$. What is the point estimate?
The midpoint is $50$.
Practice Problems
1. What is the general form of a confidence interval?
2. What does a p-value measure?
3. If a 90% CI is $(10,14)$, what is the point estimate?
4. Does a larger confidence level usually make the interval wider or narrower?
5. What are the two competing hypotheses called?
Show Answer Key
1. Estimate $\pm$ margin of error
2. How surprising the sample is under the null hypothesis
3. $12$
4. Wider
5. Null hypothesis and alternative hypothesis