Chapter 1. Statistical Significance for one proportion

Introduction

Statistical Applets

To set up the test, fill in the boxes: What is the null hypothesis about p (the numerical value you are comparing your sample result to)? Which alternative represents the question of interest, and what significance level do you require? How many observations n do you have (30,000 or fewer)?

If you already have a sample, enter the number of "successes" (X) to display the sample proportion on the graph and calculate its statistical significance. Or specify p to create a random sample from the population. Click NEW SAMPLE to generate different random samples.

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

This applet illustrates statistical tests with a fixed level of significance for a population proportion, p. The mechanics are different for other tests, but the concepts are essentially the same.

The Normal distribution shows the sampling distribution of p̂ when your null hypothesis is true and the sample size is the one you chose. The yellow area under the curve represents values of p̂ that are significant at level α. This area is equal to α.

Question 1.1

Suppose that 75% of college students prefer pepperoni on their pizzas. You took a sample of n = 150 at your college and found that 70% said they want pepperoni on their pizzas. Is this a significant result at the 10% level? Suppose you only want to know if your college is different from the rest. What information will you need to supply to perform a correct test?
P0 = jmXg31CfEDpx/x9q
n = IJaWHrT39D4=
X = Z90ZXfTCunM=
Direction: ZYXVzMECE72Lm07i28Xte9QCcFIpWz57
α = QulpcqdkKEjDcemSngVh5mL4dAw=

2
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Incorrect.
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Question 1.2

What is the P-value for this test? SHpdzvF9IgWw4MKahaF0og==

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Question 1.3

Would the null hypothesis be rejected?? AD2YBdbb6x3kfgtembjVpQ==

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Question 1.4

Suppose you had a prior belief that not many people at your college like pepperoni (because there are a lot of vegetarians at your school). What is the P-value in this case? Would the null hypothesis be rejected?
P-value = DmiFWHgSNFm3155/tNoT8A==
Decide: Yz9syaZBAR5XE1fEYuUaBy7w9KeDtnaB7mkn4g== H0

2
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Question 1.5

What percent of the time would we expect to reject this null hypothesis in this test if the proportion of people at your college who like pepperoni really is 75%? V3cqXNH6Wo7VJtVW

2
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