Question

Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (The New York Times, July 20, 2008). 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: (You may find it useful to reference the appropriate table: z table or t table).

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

• H₀: μ ≥ 350; H_A: μ < 350

• H₀: μ = 350; H_A: μ ≠ 350

• H₀: μ ≤ 350; H_A: μ > 350

c-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c-2. Find the p-value

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

d-1. What is the conclusion at the 5% significance level?

• Reject H₀ since the p-value is greater than significance level.

• Reject H₀ since the p-value is smaller than significance level.

• Do not reject H₀ since the p-value is greater than significance level.

• Do not reject H₀ since the p-value is smaller than significance level.

d-2. Should the larger computer companies be concerned?

• Yes, since we reject H₀.

• Yes, since we do not reject H₀.

• No, since we reject H₀.

• No, since we do not reject H₀.

Answer 1

(a) The Assumptions are that

(i) The sampling is a simple random sample

(ii) The population from which the sample is taken is normally distributed or approximately normally distributed

(iii) The samples are independent of each other

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(b) The Hypothesis: Since we are wanting to find if the price is less than $350

H0: 350

Ha: < 350

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(c-1) The Test Statistic:

From the data: = $342, s = $58.50, n = 6

The test statistic is given by the equation:

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(c - 2)The p Value: The p value (Left tailed) for t = -0.33, for degrees of freedom (df) = n-1 = 5, is; p value = 0.3774

Therefore Option 5: p value is 0.10

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(d - 1) Conclusion - Option 3: Do not reject H0 since the p value is greater than the significant level.

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(d -2) Option 4: No, since we do not reject H0.

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