Question

Marriage Prospects Data released by the Census Bureau in 1986 indicated the likelihood that never-married women would eventually marry. The data indicated that the older the woman, the less the likelihood of marriage. Specifically, two statistics indicated that women who were 45 and never-married had an 18 percent chance of marriage and women 25 years old had a 78 percent chance of marriage. Assume that a linear fit to these two data points provides a reasonable approximation for the function p=f(a), where p equals the probability of marriage and a equals the age of a never- married woman. (a) Determine the linear function p=f(a). (b) Interpret the slope and p intercept. (c) Do the values in part b seem reasonable? (d) If the restricted domain on this function is 20 sa s 50, determine f(20), f(30), f(40), and f(50).

Answer 1

See below

Explanation:

Using the two pairs of (a, p) to determine the function:

• (45, 18) and (25, 78)

The function would be:

• f(a) = ma + b, where m is slope, b is p-intercept

Slope is:

• m = (78 - 18)/(25 - 45) = -50/20 = -2.5

p-intercept:

• 18 = -2.5*45 + b
• b = 18 + 112.5 = 120.5

So the function is:

(a)

• f(a) = -2.5a + 120.5

(b) Slope is negative, indicating the lower probability at greater age. P-intercept of 120.5 is of the non-real case as for zero age it gives more than 100% probability.

(c) The domain needs restriction in line with law, so minimum age and maximum to be determined in order not to have unrealistic outcome. It should be ok between 18 and 48.

(d) The values at given points:

• f(20 = -2.5*20 + 120.5 = 70.5
• f(30) = -2.5*30 + 120.5 = 45.5
• f(50) = -2.5*50 + 120.5 = -4.5 (negative probability for the age of 50 is not real)