Suppose there are 8,000 people at a basketball game. You survey a random sample of 400 spectators and gather the following information: Estimate the number of women at the event.

Question

Under 30
Female: 80 | Male: 140 | Total: 220
Over 30
Female: 60 | Male: 120 | Total: 180
Total
Female: 140 | Male: 260 | Total: 400

140 women 400 women 2,800 women 8,000 women

Answer 1

To estimate the number of women at the event, we can calculate the proportion of women in the random sample of 400 spectators and then apply that proportion to the total population of 8,000 people.

In the random sample:
Number of women = 140
Total number of people in the sample = 400

Proportion of women in the sample = Number of women / Total number of people in the sample
Proportion of women in the sample = 140 / 400 = 0.35

Now, to estimate the number of women in the total population of 8,000 people:
Number of women = Proportion of women in the sample * Total population
Number of women = 0.35 * 8,000 = 2,800 women

Therefore, the estimate of the number of women at the basketball game is 2,800 women.