# Chapter 1. P-Value For A Test Of One Proportion

## Introduction

Statistical Applets To set up the test, fill in the boxes: What null hypothesis H0 about the population proportion p do you want to test? Which alternative (this represents the question) is of interest? How many observations (n) do you have (30,000 or fewer)?

If you already have a sample, enter the number of "successes" to display the sample proportion on the graph and calculate the P-value. Or you can specify the true population proportion and use the NEW SAMPLE button to create a random sample from the population, display the sample count and proportion, and calculate the P-value.

Click the "Quiz Me" button to complete the activity.

This applet illustrates the P-value for a significance test involving one population proportion, p. These concepts easily apply to any other significance test for the center of a distribution.

The Normal curve shows the sampling distribution of the sample proportion when the null hypothesis is true. The blue arrow shows in which direction the "extreme" values of will be evidence against the null hypothesis, H0 in favor of Ha.

If you change the alternate for any situation, you can see the impact on the P-value (the probability of a sample result at least as far away from the null value as that seen in the data, assuming the null hypothesis is true). ### Question 1.1

You have taken a sample of n = 1000 individuals and asked them if they typically eat breakfast. Because eating breakfast is considered healthy, you’d like to know if the proportion in the population who eat breakfast is more than two-thirds (about 67%). What is the P-value of the test if you find
(a) X = 680? UGq6HioChJyM1NqiTyn0yg==
(b) X = 700? LFY4+T3oTO8RudKkJCQHnw==

2
Try again. Make certain that your null hypothesis value and direction matched the question.
Incorrect.
Great job!

### Question 1.2

If you only asked the question of n = 20 people and found X = 15 people who eat breakfast, what is the P-value? lvCK6LJvmJ8n9fieDwXiTQ==

2
Try again. Make certain that your null hypothesis value and direction matched the question.
Incorrect.
Great job!

### Question 1.3

Which sample size will give more certain results?
n = bG25ITG1CTrTbKRq

2
Try again. What must be true for a sample proportion to be approximately Normal? Is that true here?
Incorrect.
Great job!