Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease in which one’s immune system attacks healthy cells and tissue by mistake. It is well known that lupus tends to exist more in females than in males. Researchers wondered, however, if families with a child who had lupus had a lower ratio of males to females than the general population. If this were true, it would suggest that something happens during conception that causes males to be conceived at a lower rate when the SLE gene is present. To determine if this hypothesis is true, the researchers obtained records of families with a child who had SLE. A total of 23 males and 79 females were found to have SLE. The 23 males with SLE had a total of 23 male siblings and 22 female siblings.

The 79 females with SLE had a total of 69 male siblings and 80 female siblings.

(a) Explain why this is an observational study.

(b) Is the study retrospective or prospective? Why?

(c) There are a total of 23 + 69 = 92 male siblings in the study. How many female siblings are in the study?

(d) Draw a relative frequency bar graph of gender of the siblings.

(e) Find a point estimate for the proportion of male siblings in families where one of the children has SLE.

(f) Does the sample evidence suggest that the proportion of male siblings in families where one of the children has SLE is less than 0.51, the accepted proportion of males

born in the general population? Use the α = 0.05 level of significance.

(g) Construct a 95% confidence interval for the proportion of male siblings in a family where one of the children has SLE.