<< 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

Got questions? Get instant answers now!

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"} {}
Got questions? Get instant answers now!

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

left-tailed

Got questions? Get instant answers now!

What symbol represents the Random Variable for this test?

P '

Got questions? Get instant answers now!

In words, define the Random Variable for this test.

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

Got questions? Get instant answers now!

Calculate the following:

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

  • 7
  • 100
  • 0.07
Got questions? Get instant answers now!

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

0.0293

Got questions? Get instant answers now!

State the distribution to use for the hypothesis test.

Normal

Got questions? Get instant answers now!

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'.

Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask