Statistics: Tests of Hypotheses for a Single Sample

Introduction to Hypothesis Testing

• Hypothesis testing is a statistical technique used to determine which of two competing claims about a parameter is correct.
• It involves testing a null hypothesis against an alternative hypothesis to make a decision.
• Hypothesis testing is used in engineering to solve real-world problems, such as designing an air crew escape system.

Hypothesis Testing vs. Confidence Intervals

• Hypothesis testing and confidence interval estimation are two fundamental methods used in statistical inference.
• There is a close connection between hypothesis testing and confidence intervals.

Types of Hypotheses

• A statistical hypothesis is a statement about the parameters of one or more populations.

Importance of Hypothesis Testing

• Hypothesis testing is useful in many types of decision-making problems, tests, or experiments in the engineering world.
• It provides a way to formulate and answer questions about parameters of populations.

Learning Objectives

• Structure engineering decision-making problems as hypothesis tests
• Test hypotheses on the mean of a normal distribution using Z-tests or t-tests
• Test hypotheses on the variance or standard deviation of a normal distribution
• Test hypotheses on a population proportion
• Use the P-value approach for making decisions in hypothesis tests
• Compute power and type II error probability, and make sample size selection decisions for tests on means, variances, and proportions
• Explain and use the relationship between confidence intervals and hypothesis tests
• Use the chi-square goodness-of-fit test to check distributional assumptions
• Use contingency table tests

This quiz covers tests of hypotheses for a single sample, including estimating population parameter and competing claims about the value of a parameter.