Gender in two-child families. Refer to the Human Biology (Feb. 2009) study on the gender o...

Gender in two-child families. Refer to the Human Biology (Feb. 2009) study on the gender of children in two-child families, Exercise. The article reported on the results of the National Health Interview Survey (NHIS) of 42,888 two-child families. The table below (saved in the BOYGIRL file) gives the number of families with each gender configuration

a. If it is just as likely to have a boy as a girl, find the probability of each of the gender configurations for a two-child family.

---

b. Use the probabilities, part a, to determine the expected number of families for each gender configuration.

---

c. Compute the chi-square test statistic for testing the hypothesis that it is just as likely to have a boy as a girl.

---

d. Interpret the result, part c, if you conduct the test using α = .10.

---

e. Recent research indicates that the ratio of boys to girls in the world population is not 1 to 1, but instead higher (e.g., 1.06 to 1). Using a ratio of 1.06 to 1, the researchers showed that the probabilities of the different gender configurations are: GG—.23795, BG—.24985, GB—.24985, and BB—.26235. Repeat parts b–d using these probabilities.

Gender in two-child families . Human Biology (Feb. 2009) published a study on the gender of children in two-child families. In populations where it is just as likely to have a boy as a girl, the probabilities of having two girls, two boys, or a boy and a girl are well known. Let x represent the number of boys in a two-child family.

a. List the possible ways (sample points) in which a two-child family can be gender-configured. (For example, BG represents the event that the first child is a boy and the second is a girl.)

---

b. Assuming boys are just as likely as girls to be born, assign probabilities to the sample points in part a.

---

c. Use the probabilities, part a , to find the probability distribution for x.

---

d. The article reported on the results of the National Health Interview Survey (NHIS) of almost 43,000 twochild families. The table gives the proportion of families with each gender configuration. Use this information to revise the probability distribution for x.

---

Gander Configuration	Proportion
Girl-girl (GG)	.222
Boy-girl (BG)	.259
Girl-boy (GB)	.254
Boy-boy (BB)	.265

e. Refer to part d . Find E (x) and give a practical interpretation of its value.