Small, energy-efficient, Internet-centric, new computers are increasingly gainin

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 prices as: Use Table 2. ( http://lectures.mhhe.com/connect/0078020557/Table/table2.jpg )

What assumption regarding the distribution of the price of small computers is necessary to test the analyst’s claim?

Assume that the price of small computers is (A.normally, B.not necessarily normally) distributed.

b.

Select the appropriate null and alternative hypotheses to test the analyst’s claim.

At the 5% significance level, what is the critical value? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

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 prices as: Use Table 2. ( http://lectures.mhhe.com/connect/0078020557/Table/table2.jpg )

Explanation / Answer

a) Assume that the price of small computers is (A. normally) distributed.

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of variable
H0 : = 350
HA : < 350

Hypothesis test results:

Hence,

b) Option 1 is correct.

c) Test statistic = -0.26

d - 1) Degrees of freedom = n - 1 = 6 - 1 = 5

For a left tailed test with 5 degrees of freedom and 0.05 level of significance,

Critical value = - 2.015

d - 2) Since test statistic do not lie in the rejection region, we do not reject Ho.

Hence,

Option 4 is correct.

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