[theit77]

For those of you who don't want to read the following statistical jargon, here's the jist: Somewhere between 30% and 50% of French teenagers still consider Alizée trendy.




"Alizée was mentioned yesterday on the TF1 show, "Attention à la marche!". The question was: "Out of 100 teens, how many think that Alizée is still trendy?" Answer: 40%.""


The first thing to confirm is if the show actually performed a survey. If they actually did question 100 french teenagers, then we can continue with the analysis. If the number is just an estimate... well, then it's just the show's estimate.

The population that the statistic is measuring is all teenagers in France. To confidently analyze the data, the survey must have been an SRS or Simple Random Sample and the population size must have been at least 10 times the sample size. The number of French teenagers is certainly greater than 100(10) or 1000. But an SRS is less certain. To get a Simple Random Sample, the survey would have had to randomly survey 100 teenagers out the entire population of French teenagers. This is essentially impossible to do without getting all teenagers' social security numbers, randomly choosing 100, and then forcing those 100 to answer the question. So, without a certain SRS, we can use a confidence interval, but we cannot be certain of its accuracy.

Calculation of a confidence interval: (p-hat)±z*(((p-hat)(1-(p-hat))/n)^(1/2) Where (p-hat) is the statistic of 0.4, n is 100, and z* is determined by the desired confidence interval: InvNorm((1-.95)/2)

Crunching the numbers, we find there is a 95% confidence interval of (0.30398, 0.49602). This means that we are 95% confident that the true percentage of French teenagers who still consider Alizée trendy is somewhere between 30.398% and 49.602%. A 90% confidence interval would yeild (0.31942, 0.48058), and a 99% confidence interval would yeild (0.27381, 0.52619).