Rare Events, the Sample, and the Decision and Conclusion · Exercise 18
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. 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.
(a) Is this a test of one mean or proportion?
(b) State the null and alternative hypotheses.
H_0: ____________________ H_a: ____________________
(c) Is this a right-tailed, left-tailed, or two-tailed test?
(d) What symbol represents the random variable for this test?
(e) In words, define the random variable for this test.
(f) Calculate the following:
(a) x = ________________
(b) n = ________________
(c) = _____________
(g) Calculate σ_x = __________. Show the formula setup.
(h) State the distribution to use for the hypothesis test.
(i) Find the p-value.
(j) At a pre-conceived α = 0.05, give your answer for each of the following:
(a) Decision:
(b) Reason for the decision:
(c) Conclusion (write out in a complete sentence):
Its source prints no answer for this problem, so there's nothing to check against.
OpenStax, Statistics · §9.4 Rare Events, the Sample, and the Decision and Conclusion · Exercise 18
No hints for this one.
Check your full solution
Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.
Your first check today doesn't need an account.
Your photos and PDFs are read once and not stored — only the transcription is kept.