Final answer:
To check if the pricing standard deviation is larger than claimed, calculate the sample standard deviation and use a hypothesis test at a 5 percent significance level. If it is significantly higher, it suggests price variability and may affect purchasing decisions.
Step-by-step explanation:
To determine if the pricing has a larger standard deviation than claimed by the manufacturer, we need to calculate the standard deviation of the sample provided and compare it with the manufacturer's claim of $25. The price comparison shows the following values: $1,299; $1,229.99; $1,193.08; $1,279; $1,224.95; $1,229.99; $1,269.95; and $1,249. We can calculate the sample standard deviation, then use a hypothesis test to compare it to the claimed population standard deviation. At a 5 percent significance level, we would reject the null hypothesis that the sample comes from a population with a $25 standard deviation if the calculated sample standard deviation is significantly higher than $25, considering the degrees of freedom and corresponding t-value.
As a potential buyer, the practical conclusion from the analysis would be whether or not the prices you're seeing online are significantly more variable than what the manufacturer suggests. If they are, this could indicate that there might be better deals available, or it could suggest price instability, which might affect your purchasing strategy.