Final answer:
To evaluate the claim of the manufacturer about the standard deviation of the computer prices, one would perform a hypothesis test using the chi-square distribution. If the calculated value exceeds the critical value at the 5 percent significance level, the null hypothesis is rejected, suggesting a larger standard deviation than $25. As a buyer, considering price variability along with other factors is crucial.
Step-by-step explanation:
To determine whether the pricing has a larger standard deviation than claimed by the manufacturer for the specific computer, we can perform a hypothesis test.
The null hypothesis ('H_0') is that the standard deviation of the computer price is $25. To test this hypothesis, we will use the sample standard deviation of the prices listed: $1,299; $1,229.99; $1,193.08; $1,279; $1,224.95; $1,229.99; $1,269.95; and $1,249.
Given the sample size (n = 8) and the sample data, we would calculate the sample standard deviation and then use the chi-square (χ²) distribution since the actual population standard deviation is unknown.
If the calculated chi-square value is greater than the critical value at the 5 percent significance level, we would reject the null hypothesis, indicating that there is a larger standard deviation than $25.
As a potential buyer, a practical conclusion would be to look at the variability of the prices and decide on a retailer based on the best price found while also considering other factors such as warranty, return policy, and customer service.