Question

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 31 couples. Complete parts​ (a) through​ (c) below.

a. Find the mean and the standard deviation for the numbers of girls in groups of 31 births.

b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

Values of ___ girls or fewer are significantly low. ​(Round to one decimal place as​ needed.)

Values of ___ girls or greater are significantly high. (Round to one decimal place as​ needed.)

c. Is the result of 31 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

The result is/is not significantly​ high, because 31 girls is greater than/equal to/less than ___ girls. A result of 31 girls would suggest that the method is not effective/is effective.​(Round to one decimal place as​ needed.)

Answer 1

p = 0.5

n = 31

a) mean = n * p = 31 * 0.5 = 15.5

standard deviation = sqrt(n * p * (1 - p)) = sqrt(31 * 0.5 * 0.5) = 2.78

b) Significantly low value = mean - 2 * sd = 15 - 2 * 2.78 = 9.44

Significantly low value = mean + 2 * sd = 15 + 2 * 2.78 = 20.56

c) The result is significantly high, because 31 girls is is greater than 20.6 girls. A result of 31 girls would suggest that the method is not effective