CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 8. Hypothesis Testing

8.2 Testing a Proportion Hypothesis

Learning Objectives

• Test a hypothesis about a population proportion by applying the binomial distribution approximation.


• Test a hypothesis about a population proportion using theP-value.


• Test a hypothesis about a population proportion using confidence intervals.

Introduction

For most hypotheses that we will study, we use the general formula for calculating the test statistic:

Test Statistic=

Observed Sample Mean-Population Mean

Standard Error

or, the familiar

z=

X ̄−μ 0

σx

This formula helps us determine the magnitude of the difference between the observed sample mean and the
hypothesized population mean. However, many times in statistics we study or make inferences aboutproportions
of a population. For example, when we look at election results we often look at the proportion of people that vote
and who this proportion of voters will choose. Typically, we call these proportionspercentagesand we would say
something like “Approximately 68 percent of the population voted in this election and 48 percent of these voters
voted for Barak Obama.”

So how do we test hypotheses about proportions? We use the same process as we did when testing hypotheses
about populations but we must includesample proportionsas part of the analysis. This lesson will address how we
investigate hypotheses around population proportions and how to construct confidence intervals around our results.

Hypothesis Testing about Population Proportions by Applying the Binomial Distri-

bution Approximation

As mentioned, we perform hypothesis tests about population proportions (often called percentages) quite often. We
could perform these tests in the following examples:

• What percentage of graduating seniors will attend a 4−year college?


• What proportion of voters will vote for John McCain?


• What percentage of people will choose Diet Pepsi over Diet Coke?