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: $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; HA: μ < 350 H0: μ = 350; HA: μ ≠ 350 H0: μ ≤ 350; HA: 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.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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:


$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.

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