Question

Note: you can copy any of the following symbols from here: a p 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.)

Answer 1

Accept a false null hypothesis. The true proportion of people who will develop schizophrenia is different from 0.004. Excel add-in ( Mega Stat) procedure:

Step 1: In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests. Step 2: Choose Proportion vs. Hypothesized Value. Step 3: Choose Data Input. Step 4: In Observed, enter the value 17 under x and enter the value 3000 under n. Step 5: In Hypothesized, enter the value 0.004 under p. Step 6: Choose not equal in alternative. Step 7: Click OK Excel add-in (Mega Stat) output: Hypothesis test for proportion vs hypothesized value Observed Hypothesized 0.0057 0.004 p (as decimal) 17/3000 12/3000 p (as fraction) 17. 12. X 3000 3000 n 0.0012 std. error 1.45 z .1481 p-value (two-tailed) 0.003 confidence interval 95.% lower 0.0084 confidence interval 95.% upper 0.0027 margin of error

The value of test statistic is z =1.45. P-value = 0.1481. Since p-value( = 0.1481) > a(=0.05), do not reject the null hypothesis. Therefore, we can conclude that the true proportion of people who will develop schizophrenia is 0.004. The 95% confidence interval is 0.003 < p <0.0084. Yes, 0.004 is within the interval.