Chapter 10.5, Problem 11IP

To determine

To calculate: The number of people expected to buy T-shirts at the next concert and if sampling method valid

Answer to Problem 11IP

The sampling method is valid. 1225 people would be expected to buy T-shirts at the next concert.

Explanation of Solution

Given information: 140 of 800 people would by the T-shirts and 7000 people will attend the next concert.

Calculation:

The people are chosen in a pattern of one out of tenth person is surveyed. So it is a systematic random sample. So the sampling method is valid.

Since 140 out of 800 would by the T-shirt and 7000 people will attend the next concert we can write the proportion as,

  $\frac{140}{800}=\frac{x}{7000}$

Where $x$ is number of people who may likely to buy the T-shirt.

  $140*7000=x*800$

  $8x=9800$

  $x=1225$ .

So out of 7000 people 1225 people would likely buy T-shirt at the next concert.