Chapter 8: Hypothesis Tests for One Population Mean


Recall that inferential statistics includes estimation and hypothesis testing. Chapter 7 introduces point estimates and confidence intervals (estimation) for the population mean [latex]\mu[/latex]. This chapter introduces hypothesis tests for the population mean [latex]\mu[/latex]. Hypothesis tests are used to test statements about the value of the population mean [latex]\mu[/latex]. For example:

  • A certain brand of energy-saving light bulb advertises that its bulbs last at least 15,000 hours. A contractor suspects this claim is invalid, and he wishes to test if the mean lifespan of bulbs is less than 15,000 hours.
  • A factory produces bottles of lotion that are intended to contain 100 ml of lotion. A factory worker performs regular tests to determine if the average volume of bottles differs from 100ml.
  • A popular pizzeria wishes to ensure speedy service to customers, so the franchise strives to ensure that its average delivery time is below 30 minutes. After receiving a complaint regarding slow service, the owner decides to conduct a test to see if the average delivery time is above 30 minutes.

Hypothesis tests provide a formal tool that can be used to measure the strength of evidence supporting your suspicions.

Learning Objectives

As a result of completing this chapter, you will be able to do the following:

  • Write down the null and alternative hypotheses for a study.
  • Explain the difference between the type I and the type II errors and the relationship between these two types of errors.
  • Define the P-value, both mathematically and in plain English.
  • Distinguish between the one-mean Z and the one-mean t-test, and identify when each test should be used.
  • Conduct a one-mean Z test and a one-mean t-test using the P-value or critical value approaches.
  • Calculate the P-value or the range of the P-value for a hypothesis test.
  • Explain the relationship between confidence intervals and hypothesis tests.


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