In the article “The impact of obesity on illness absence and productivity in an industrial population of petrochemical workers” published in the journal Annals of Epidemiology (Tsai et al., 2008), the authors studied the relationship between body mass index (BMI) and illness and absence from work. Table 5.12 was extracted from this article and contains a summary of the 3612 males and 541 females in the study according to the BMI categories 18.5 ≤ BMI ≤ 24.9, 25 ≤ BMI ≤ 29.9, and BMI ≥ 30. Use the information in Table 5.12 to answer the following:

(a) Estimate the proportion of males having BMI greater than or equal to 30.

(b) Compute the estimated standard error for the estimate of the proportion of males having BMI greater than or equal to 30.

(c) Based on the observed data what are the most likely values of the proportion of males having BMI greater than or equal to 30.

(d) Does the observed sample provide any evidence that the proportion of males having BMI greater than or equal to 30 is at least 0.40? Explain.