Final answer:
To test if the standard deviation of computer prices is greater than the claimed $25 by the manufacturer, we calculate the sample standard deviation and perform a hypothesis test using the chi-square distribution at a 5 percent significance level. A potential buyer would conclude that more variability in pricing suggests the possibility of finding the computer at better deals.
Step-by-step explanation:
To determine if the standard deviation of computer prices is larger than the manufacturer's claim, we first calculate the sample standard deviation from the website's price data. The sample contains the following prices: $1,299; $1,229.99; $1,193.08; $1,279; $1,224.95; $1,229.99; $1,269.95; and $1,249. The manufacturer's claimed standard deviation is $25.
To perform a hypothesis test, we set our null hypothesis as: the population standard deviation is $25. The alternative hypothesis is that it's greater than $25. Using the sample standard deviation and the chi-square distribution, we can compare the calculated test statistic to the critical value at a 5 percent significance level. If the test statistic exceeds the critical value, we reject the null hypothesis, indicating that the pricing likely has a larger standard deviation than claimed.
As a potential buyer, if we find that the standard deviation is indeed larger, it suggests there may be more variability in pricing than the manufacturer indicates. This could mean that there might be a chance to find the computer at prices significantly lower or higher than the average claimed price, which could influence purchasing decisions.