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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