One-Sample Tests of Hypothesis

Overview

Goals

Statistical hypothesis tests are important for quantifying answers to questions about samples of data. The interpretation of a statistical hypothesis test requires a correct understanding of p-values and critical values. Regardless of the significance level, the finding of hypothesis tests may still contain errors.

Learning Objectives

At the end of the chapter, you will be able to: LO1 Define a hypothesis. LO2 Explain the five-step hypothesis-testing procedure. LO3 Describe Type I and Type II errors. LO4 Define the term test statistic and explain how it is used. LO5 Distinguish between a one-tailed and a two-tailed test of hypothesis. LO6 Conduct a test of hypothesis about a population mean. LO7 Compute and interpret a p-value. LO8 Conduct a test of hypothesis about a population proportion. LO9 Compute the probability of a Type II error.

Context

A bearing used in an automotive application is supposed to have a nominal inside diameter of 2.5 cm. A random sample of 36 bearings is selected and the average inside diameter of these bearings is 2.495 cm. Bearing diameter is known to be normally distributed with standard deviation OF 0.02 cm. (a) Analyse the hypotheses H0: µ= 2.5 versus H1: µ ≠ 2.5 using α = 0.01. (b) Calculate the P-value of the test statistic computed in part (a)