he cost of a one

-

carat VS2 clarity, H color diamond from the Diamond Source USA is $4000

(

www.diasource.com

, July 2000). A Midwestern jeweler makes calls to contacts in the diamond

district of New York City to see whether the mean price of similar

diamonds differs from $4000.

The jeweler agrees to collect cost data from 14 New York City contacts (ignore the fact that the

sample is really too small on this problem and some of the others...the goal here is to get the

process down).

a.

Formulate the nul

l and alternative hypotheses that can be used to determine if the

mean price in New York City differs from $4000.

b.

Using

a

= .01, what are the critical values for the test?

c.

Assume the sample of 14 provides a sample mean price of $4160 and a sample sta

ndard

deviation of $275. Compute the value of the test statistic.

d.

What is your conclusion (use the critical value approach for this part)?

e.

What can you say about the

p

-

value?