# Chapter 8: Hypothesis Tests for One Population Mean

**Overview**

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.

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.