<< Chapter < Page Chapter >> Page >
This module provides a practice of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student learning outcomes

  • The student will conduct a hypothesis test of a single population proportion.

Given

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. (http://www.nimh.nih.gov/publicat/depression.cfm) Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

Hypothesis testing: single proportion

Is this a test of means or proportions?

Proportions

State the null and alternative hypotheses.

  • H o : size 12{H rSub { size 8{O} } :} {}
  • H a : size 12{H rSub { size 8{a} } :} {}
  • H o : p = 0 . 095 size 12{H rSub { size 8{O} } :p=0 "." "095"} {}
  • H a : p < 0 . 095 size 12{H rSub { size 8{a} } :P<0 "." "095"} {}

Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

left-tailed

What symbol represents the Random Variable for this test?

P '

In words, define the Random Variable for this test.

the proportion of people in that town surveyed suffering from depression or a depressive illness

Calculate the following:

  • x = size 12{x={}} {}
  • n = size 12{n={}} {}
  • p ' =

  • 7
  • 100
  • 0.07

Calculate σ p ' . Make sure to show how you set up the formula.

0.0293

State the distribution to use for the hypothesis test.

Normal

Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized mean and the sample proportion, p-hat. Shade the area corresponding to the p-value.

Blank horizontal axis of P'.

Find the p-value

0.1969

At a pre-conceived α = 0 . 05 size 12{α=0 "." "05"} {} , what is your:

  • Decision:
  • Reason for the decision:
  • Conclusion (write out in a complete sentence):

  • Do not reject the null hypothesis

Discusion question

Does it appear that the proportion of people in that town with depression or a depressive illness is lower than general adult American population? Why or why not?

Get the best College algebra course in your pocket!





Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics (custom lecture version modified by t. short)' conversation and receive update notifications?

Ask