This lesson explains how to select and conduct hypothesis tests that compare two population means or two population proportions. The activities use stock-market data, candy packages, and class surveys to illustrate the choices involved.
A hypothesis test starts with a question about a population parameter. For two population means, the parameter is a difference such as μ₁ − μ₂. For two population proportions, it is a difference such as p₁ − p₂. Define the groups and parameter clearly before writing hypotheses.
All flashcards
When are two samples paired?
They are paired when observations are matched, such as measurements on the same stock on two days. Analyze the within-pair differences.
Which test compares two independent proportions?
A two-proportion z test, provided the sampling and success/failure conditions support the normal approximation.
Which test is a sensible default for two independent means?
Welch’s two-sample t test. It compares the means without requiring the population variances to be equal.
How is a paired t test constructed?
Calculate one difference per matched pair, then conduct a one-sample t test on the mean of those differences.
What does failing to reject the null hypothesis mean?
The data do not provide sufficient evidence against the null at the chosen significance level. It does not prove that the null is true.
Quiz questions
Which test compares the increase rates of independently selected NYSE and NASDAQ stocks when the success/failure conditions are met?Answer: A two-proportion z test.
Why should measurements from the same eight stocks on two consecutive days be analyzed as paired data?Answer: Each stock’s measurements are matched, so the analysis uses within-stock changes.
If a stock’s change is defined as day-two value minus day-one value, which alternative tests whether stocks went down on average on day two?Answer: Ha:μd<0.
What does a p-value represent in a hypothesis test?Answer: The probability of an equally or more extreme result, assuming the null hypothesis is true.
A test has p-value 0.03 and significance level α=0.05. What is the appropriate decision?Answer: Reject the null hypothesis because the p-value is below the significance level.
Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.