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10.14 Practice 3: single proportion

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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?
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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