Question

To increase attendance, the marketing department for a major league baseball team targeted advertising toward families, children, and females in order to attract more attendees. Past figures showed an average per game of 58% male (age 12 and over), 28% female (age 12 and over), and 14% children (under 12). Therefore, in the past, an average per game of 42% were female or children and the goal of the advertising was to improve that percentage. After two months of advertising, the marketing director reported an average per game of 54% of the attendees were either females or children under 12.

1) Observe the statistics below and either verify or dispute the director's claim. Include in your work the answer to the following question: If a fan is randomly selected, what is the probability of selecting a woman or a child under 12? Show, in detail.

2) How large would you say the increase in the number of females and children under 12 must be in order to say that the advertising worked? Does any increase indicate improvement, or would there have to be a significant amount? If a significant amount, what would you consider a significant amount in this case?

All attendees Average per game over the past two months (all ages):

Males (all) 19,600

Females (all) 10,400

Total 30,000

Children under 12 Average per game over the past two months:

Boys (under 12) 3,100

Girls (under 12) 2,700

Total 5,800

Answer 1

1)Females( 12 and over) = 10400 -3100 = 7700

Children (under 12 ) = 3100+2700 = 5800

Total female and children = 7700+5800 = 13500

Total = 30,000

Probability selecting a woman or child under 12 = (7700+5800) / 30000= 0.45 or 45%

As we can see that only 45% of attendees were either female  or child

we can dispute the director's claim

2) In the past 42% of attendees were either female  or child

42% of 30000 = 12600

According to director's claim 54% of attendees were either female  or child

54% of 30000= 16200

So , 16200-12600 = 3600 increase in number of attendees in order to say advertising worked

In actual , number of female or child attendees = 13500

So there is 13500--12600 = 900 increase in female and children attendees

This is not significant amount

The significant amount is 3600 increase in female and children attendees