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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Prasenjit
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.