A Popular Music Magazine Has Speculated That the Average Length

question 46

Essay

A popular music magazine has speculated that the average length of a song on one of today's popular CDs is 3.75 minutes with a standard deviation of 0.75 minutes.A randomly selected song of a particular new type of music is 5 minutes.Using the .05 level of significance,is this new type of music,represented by this one song,longer than popular songs in general?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with graphs of distributions,the mean,standard deviation,Z scores,the normal curve and normal curve tables,and the basics of probability,but knows nothing else about statistics.Be sure your explanation includes the overall logic of hypothesis testing including each of the five steps.

---

Definitions:

Human Exceptionalism

The attitude that humans are exempt from natural ecological limits.

Malthusian Theorem

A principle asserting that population growth tends to outpace the growth of food supply, leading to periodic famine, poverty, and population checks such as disease and war.

Conservation

The protection and preservation of the natural environment and wildlife, ensuring sustainable use of resources for future generations.

Conservation Era

A period of American environmental history, primarily in the late 19th and early 20th centuries, marked by increasing awareness and efforts to conserve natural resources.