Question

A student has a large digital music library. The mean length of the songs is 258 seconds with a standard deviation of 87 seconds. The student creates a playlist that consists of 30 randomly selected songs.

a.Is the mean value of 258 seconds a parameter or a statistic? Explain.

b.What should the student expect the average song length to be for his playlist?

c.What is the standard error for the mean song length of 30 randomly selected songs?

d.Would a playlist of 50 songs have a standard error that is greater than or less than your answer to part c? Explain.

Answer 1

Answer a)

The mean value of 258 seconds is a parameter because it represents the mean length of all songs in library.

Answer b)

Expected mean is equal to the population mean. So, the student should expect the average song length of 258 seconds.

Answer c)

Standard Error = σ/Sqrt(n)

Substituting σ = 87 and n = 30 in the formula, we get

Standard Error = 87/sqrt(30)

Standard Error = 15.8840

Answer d)

In the formula of standard error, we can see that the sample size is in denominator. So if sample size increase standard error decreases. So, a playlist of 50 songs will have a less standard error as compared to Part c.

For 50 songs playlist, Standard Error = 87/sqrt(50) = 12.3037 <  15.8840