Hypothesis Testing of Single Mean and Single Proportion: Practice 3 1.6 2008/06/22 19:06:37 GMT-5 2008/08/15 12:04:21.880 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics 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 explore the properties of hypothesis testing with a single 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 averages or proportions? Proportions State the null and alternative hypotheses. aHo: size 12{H rSub { size 8{O} } :} {} b Ha: size 12{H rSub { size 8{a} } :} {} a H o : p = 0 . 095 size 12{H rSub { size 8{O} } :p=0 "." "095"} {} b 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-hat In words, define the Random Variable for this test. the proportion of people in that town suffering from depress. or a depr. illness Calculate the following: ax= size 12{x={}} {} b n= size 12{n={}} {} c p-hat= a7 b100 c0.07 Calculate σx. Make sure to show how you set up the formula. 2.93 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. Find the p-value 0.1969 At a pre-conceived α=0.05 size 12{α=0 "." "05"} {}, what is your: a Decision: b Reason for the decision: c Conclusion (write out in a complete sentence): aDo 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?