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.
${H}_{o}:$
${H}_{a}:$
${H}_{o}:p=0\text{.}\text{095}$
${H}_{a}:p<0\text{.}\text{095}$
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?
$\text{P}\text{'}$
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:
$x=$
$n=$
$\text{p}\text{'}=$
7
100
0.07
Calculate
${\sigma}_{p\text{'}}$ . 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.
Find the
p-value
0.1969
At a pre-conceived
$\alpha =0\text{.}\text{05}$ , 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?
Questions & Answers
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