Probability & Statistical Inference Lecture 7

MSc in Computing (Data Analytics)

General Steps in Hypotheses testing1. From the problem context, identify the parameter

of interest.

2. State the null hypothesis, H0 .

3. Specify an appropriate alternative hypothesis, H1.

4. Choose a significance level, .

5. Determine an appropriate test statistic.

6. State the rejection region for the statistic.

7. Compute any necessary sample quantities, substitute these into the equation for the test statistic, and compute that value.

8. Decide whether or not H0 should be rejected and report that in the problem context.

Testing the difference between two sample means

• It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance.

Type of questions that can be answered with Two sample hypothesis tests. A manufacturing plant want to compare the q whether the test results of patients who

received a drug are better than test results of those who received a placebo.

The question being answered is whether there is a significant (or only random) difference in the average cycle time to deliver a pizza from Pizza Company A vs. Pizza Company B.

Difference in Means of Two Normal Distributions, Variances Known

Test Assumptions

Example

Example

Example

Confidence Interval on a Difference in Means, Variances Known

Example

Example

Difference in Means of Two Normal Distributions, Variances unknown

We wish to test:

Case 1: 22

221

The pooled estimator of 2:

Difference in Means of Two Normal Distributions, Variances unknown

Example

Example

Example

Confidence Interval on the Difference in Means, Variance Unknown

Case: 22

221

Example

Example

Example

Some Practical Examples