Question

Note: you can copy any of the following symbols from here: u p o g? 2 s # It has been reported that the probability that an individual will develop schizophrenia over their lifetime is 0.004. Medical researches selected a random sample of 3000 individuals and determined that 17 of them developed schizophrenia. Is there evidence to support the claim that the true proportion of people who will develop schizophrenia is different from 0.004 at the a = 0.05 level of significance? (Source: Saha S, Chant D, Welham J, McGrath J. A systematic review of the prevalence of schizophrenia. PLoS Med 2(5): e141.) a. Determine the null and alternative hypotheses: H1: b. What type of test is being conducted in this problem? c. What parameter is being tested? d. Explain what it would mean to make a Type I error e. Explain what it would mean to make a Type Il error. Suppose the null hypothesis is rejected. State the conclusion based on the results of the test.

Answer 1

In order to test if the proportion of people who develop schizophrenia is different from 0.004 our hypothesis is:

a. H0: p= 0.004

vs H1: p not equal 0.004

b. The test being used in this problem is one proportion z test.

c. The parameter being tested is the population proportion p

d. A type I error is rejecting a true null hypothesis. So here it would be concluding that p not equal 0.004 when it actually is.