Question: Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (New York Times, July 20, 2008). These computers, often called netbooks, have scant onboard memory and are intended largely for surfing websites and checking e-mail. Some of the biggest companies are wary of the new breed of computers because their low price could threaten PC makers' already thin profit margins. An analyst comments that the larger companies have a cause for concern since the mean price of these small computers has fallen below $350. She examines six popular brands of these small computers and records their retail price as:
$322 $269 $373 $412 $299 $389
a. What assumption regarding the distribution of the price of small computers is necessary to test the analyst's claim?
b. Specify the appropriate null and the alternative hypotheses to test the analyst's claim.
c. Calculate the value of the test statistic.
d. At the 5% significance level, what is the critical value(s)? What is the conclusion to the test? Should the larger computer companies be concerned?