Question

The Genetics & IVF Institute in Fairfax, Virginia, have developed a technique called MicroSort that claims to increase the chances of a couple to have a baby of a specified gender. The method for increasing the likelihood of a girl is referred to as XSORT and for increasing the likelihood of a boy is called YSORT. In a clinical trial, 945 couples requested baby girls and therefore were given the sperm form the XSORT method. Out of the 945 couples, 879 of them had a baby girl. In this case study, we will work toward answering the question: “Is the XSORT method effective in increasing the chance of a baby girl being born?” Questions with lines are expecting only an answer on the line while those without lines expect a sentence or two of explanation or computations.

1) What would be the expected value for the number of girls born out of 945 births in the XSORT method had no effect?

2) Using your answer to number (1), what is your initial option on whether the XSORT method is effective? (No statistics/calculations needed. Simply state your opinion and why.)

Before we continue to create the statistical argument to answer our question of the effectiveness of the XSORT method, we will take some time working with only two births. 3) So, the discrete random variable for our probability model would be X = number of ___________ in two births. (Fill in the blank.)

4) State the probability distribution for the number of (answer to (3)) in two births. Be sure to show that the two properties required for a probability distribution are satisfied.

5) Create the associated probability histogram.

Answer 1

1) What would be the expected value for the number of girls born out of 945 births in the XSORT method had no effect?

Assuming that boys and girls have equal probability, expected value for the number of girls born out of 945 births

= 945 * 0.5 = 472.5

2)

As, the observed number of girls born out of 945 births by  XSORT method is 879 which is greater than 472.5, the initial option is that the XSORT method is effective.

3)

The discrete random variable for our probability model would be X = number of girl child in two births.

4)

Probability of girls born by XSORT method = 879 / 945 = 0.93

For 2 births,

Probability of no girls born = (1 - 0.93) * (1- 0.93) = 0.0049

Probability of 1 girls born = 2 * 0.93 * (1- 0.93) = 0.1302

Probability of 2 girls born = 0.93 * 0.93 = 0.8649

The probability distribution for the number of girl child in two births.

P(X = 0) = 0.0049

P(X = 1) = 0.1302

P(X = 2) = 0.8649

5)

The probability histogram is,