Question

Q2. FIFA’s world cup

Although Women world cup viewers are growing rapidly (764 Million TV views in Canada 2015), it is still far from getting close to Men’s (3.5 Billion TV views in Russia 2018). The ticket prices are also different. The Federation Internationale de Football Association (FIFA) sets the official prices of tickets. Let’s concentrate on the prices of final matches in men’s world cup, Russia 2018 and women’s world cup, France 2019.

A seat for the final match in Russia 2018 cost from 455 to 1100 USD ( with mean of 600 USD and standard deviation of 200 USD). A seat for Women’s France 2019 cost from 25 to 95 USD (with the mean of 60 USD and standard deviation of 20 USD). Both data are slightly skewed to the right.

A journalist wanted to write a report about the differences between Men and Women world cups. He headed to bars after the finals and interviewed spectators who came for a drink after the game. In each bar, he asked spectators how much they paid for their tickets. Then, he recorded the name of the bar, number of people he interviewed and the average ticket price. In each bar in Moscow where the final of Russia 2018 took place, he interviewed 50 spectators. He interviewed 10 people in each bar in Lyon where the final of France 2019 took place. He started his analysis by preparing the histograms of the mean ticket price for Russia 2018 and France 2019. (Hint. Assume spectators’ going to bar was at random)

1. What do you think the data distribution look like for the histogram of the mean ticket price of Russia 2018? Justify your answer.( 2 points)
2. What do you think the data distribution look like for the histogram of the mean ticket price of France 2019? Justify your answer.(2 points)
3. What’s the probability that the mean of ticket prices of the spectators in bars after the Russia 2018 final was between 550 and 650 USD? (6 points)

Answer 1

a.

The data distribution for the histogram of the mean ticket price of Russia 2018 looks like a normal distribution because the Central Limit Theorem(CLT) is applicable as the sample size, n is large enough (n =50 > 30). So, irrespective of the original population distribution, the distribution of the sample mean is normally distributed.

b.

The data distribution for the histogram of the mean ticket price of France 2019 looks like a slightly right skewed distribution because the original population distribution is slightly right skewed and we cannot apply the Central Limit Theorem(CLT) as the sample size, n is small (n =10 < 30).

c.

Mean, =600 USD

Standard deviation, =200 USD

Sample size, n =50

Z =(​​​​​​)/(​​​​​​)

Z =(550 - 600)/(200/​​​​​​) = -1.7678

Z =(650 - 600)/(200/​​​​​​) =1.7678

The probability that the mean of ticket prices of the spectators in bars after the Russia 2018 final was between 550 and 650 USD = P(550 < < 650) =P(-1.7678 < Z < 1.7678) =0.9229