• What is statistics? Making an inference about a population from a sample. • What is the logic that allows you to be 95% confident that the confidence interval contains the population parameter?

We know from the CLT that sample means are normally distributed around the real population mean (). Any time you have a sample mean within E (margin of error) of then the confidence interval will contain . Since 95% of the sample means are within E of then 95% of the confidence interval constructed in this way will contain.

• Why do we use confidence intervals verses point estimates? The sample mean is a point estimate (single number estimate) of the population mean – Due to sampling error, we know this is off. Instead, we construct an interval estimate, which takes into account the standard deviation, and sample size.

– Usually stated as (point estimate) ± (margin of error)

• What is meant by a 95% confidence interval? That we are 95% confident that our calculated confidence interval actually contains the true mean.

• What is the logic of a hypothesis test?

“If our sample result is very unlikely under the assumption of the null hypothesis, then the null hypothesis assumption is probably false. Thus, we reject the null hypothesis and infer the alternative hypothesis.”

• What is the logic of using a CI to do a HT?

We are 95% confident the proportion is in this interval… if the sample mean or proportion is in the confidence interval the null hypothesis could be inferred. Else, the alternative hypothesis would.

• What is the predictable distribution for proportions? Why? “Proportions follow a normal distribution provided: n·p ≥ 5 and n·(1– p) ≥ 5 ( Rule of 5 ) Thus the test statistic that we use is: • Can 1000 people represent 2 million? Why? Yes, depends how confident you want to be… to be +or- 1% (95% confident)

•If Ho: μ ≤ 50 and our sample mean was 51.3, why don’t we just