Final answer:
To determine the minimum detectable effect on obesity from the offer of a housing voucher in the MTO experiment, an ITT analysis would be used with known population mean, standard deviation, power, and significance level, applying a formula involving Z-scores which require statistical software or tables to find exact values.
Step-by-step explanation:
To analyze the impact of providing a housing voucher on the prevalence of clinical obesity in the Moving to Opportunity (MTO) experiment, we use statistical hypothesis testing. Given the population mean prevalence of obesity (μ) is 0.586 with a standard deviation (σ) of 0.493, we want to detect the minimum intervention effect (d) for a power of 80% (1-β), at a 5% significance level (α), for a one-tailed test. To calculate this, we use the formula for the minimum detectable effect (MDE) in an intention-to-treat (ITT) analysis: MDE = (Z₁-β + Zα) * (σ / √n), where Z₁-β and Zα are the Z-scores corresponding to the power and significance level respectively, and n is the sample size of the combined treatment group. Unfortunately, without the exact Z-scores or a statistical software or table to find these values, the exact minimum detectable ITT effect cannot be determined here.