Statistical Methods- Lecture 10-11

Question 1

What does the CLT tell us?

Answer 1

The CLT tells us that under certain conditions the sampling distribution will be approximately normal

Question 2

How do we construct a confidence interval?

Answer 2

Point estimate +- z* x SE

An approximate 95% confidence interval is
Point Estimate +- 1.96 x SE

Question 3

What is the margin of error?

Answer 3

In a confidence interval, z* x SE is called the margin of error

Question 4

What are the interpretations of confidence intervals?

Answer 4

Confidence intervals are…

• always about the population (not the sample)
• only about population parameters, not individual observations
• only reliable if the sample statistic they’re based on is an unbiased estimator of the population parameter

Question 5

What is a hypothesis test similar to?

Answer 5

Hypothesis testing is very much like a court trial
H0: Defendant is innocent
HA: Defendant is guilty

If we fail to reject the null hypothesis, we never declare the null hypothesis to be true because we do not know if it is or not. Similar to a judge saying a verdict of not guilty as there is not enough evidence to declare them guilty.

Question 6

How do you conduct a hypothesis test?

Answer 6

We assume that the null hypothesis is true. If the test results suggest that the data do not provide convincing evidence for the alternative hypothesis, we stick with the null hypothesis

Question 7

What are the steps in a hypothesis test?

Answer 7

• specify H0 and HA and significance level
• state the assumptions of the data
• specify a test statistic
• either rejection region or p-value

Question 8

What is the rejection region in hypothesis testing?

Answer 8

Using HA, define a rejection region of values of the test statistic that are “extreme” under H0 in the direction of HA. If the observed test statistic is within RR then reject the null hypothesis in favor of the alternative hypothesis, otherwise fail to reject the null hypothesis

Question 9

How do you calculate the p-value in hypothesis testing?

Answer 9

Calculate the p-value under the null hypothesis. The p-value will be the probability of the event that the test statistic is the observed value of more extreme. If the p-value < (significance level) then reject the null hypothesis in favor of the alternative hypothesis, otherwise fail to reject the null hypothesis