Choose the best interpretation of these results.

Question

A popular music magazine has determined that the average length of a song is 3.75 minutes. A random sample of 50 songs of a new age instrumental genre is 4 minutes with a standard deviation of 0.75 minutes. Using the 5% level of significance, is this new type of music different in length than songs in general? Choose the best interpretation of these results.

Answer 1

THe test statistic is :

 

  X-bar - U

 -------------

      stdev/square-root(N)

 

X-bar is the sample mean which is 4 minutes

the population mean, per status quo, is 3.75

the standard deviation is 0.75

n = 50

 

so the test statistic is ( 4 - 3.75) /  (0.75/square-root(50) = 2.35

 

The 95% confidence level means, the rejection threshold cutoff

is 1.96.

 

The test statistic is greater, so yes, there is statistical evidence

that the average lengths of the 50 songs in this sample

is "different" , or greater than the norm