Question

You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of $1,249 with a very narrow standard deviation of $25. You find a website that has a price comparison for the same computer at a series of stores as follows: $1,299; $1,229.99; $1,193.08; $1,279; $1,224.95; $1,229.99; $1,269.95; $1,249. Can you argue that pricing has a larger standard deviation than claimed by the manufacturer? Use the 5% significance level. As a potential buyer, what would be the practical conclusion from your analysis?

a) The pricing has a larger standard deviation than claimed.

b) The pricing has a smaller standard deviation than claimed.

c) Cannot be determined.

d) The practical conclusion would be to buy the computer.

Answer 1

The analysis concludes that the pricing does not significantly deviate from the claimed standard deviation.

To determine whether the pricing has a larger standard deviation than claimed by the manufacturer, we need to perform a hypothesis test using the 5% significance level.

The null hypothesis (H0) is that the standard deviation of the prices is equal to $25, and the alternative hypothesis (Ha) is that the standard deviation is greater than $25.

We can use the Chi-square test statistic to test this hypothesis.

First, we calculate the sample standard deviation of the prices from the website data, which is $44.39.

Then, we calculate the test statistic, which is given by
`(n-1)s^2/\sigma^2`, where n is the sample size, s is the sample standard deviation, and σ is the claimed standard deviation ($25).

The test statistic is approximately 5.84.

Comparing this test statistic to the critical value (χ^2α,n-1 = 15.086), we find that the test statistic is less than the critical value.

Therefore, we fail to reject the null hypothesis.

So, we cannot argue that the pricing has a larger standard deviation than claimed by the manufacturer.

The practical conclusion from this analysis would be that the pricing does not significantly deviate from the claimed standard deviation of $25.