Rare Events, the Sample, Decision and Conclusion · Exercise 18

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5% 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) $p^{{}^{\prime }}$ = _____________
(g) Calculate σ_x = __________. Show the formula set-up.
(h) State the distribution to use for the hypothesis test.
(i) Find the p-value.
(j) At a pre-conceived α = 0.05, what is your:
(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, Introductory Statistics 2e · §9.4 Rare Events, the Sample, Decision and Conclusion · Exercise 18