<< Chapter < Page | Chapter >> Page > |
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.
Is this a test of means or proportions?
Proportions
State the null and alternative hypotheses.
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:
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:
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?
Notification Switch
Would you like to follow the 'Collaborative statistics (custom lecture version modified by t. short)' conversation and receive update notifications?