Question

Suppose that you are responsible for making arrangements for a business convention and that you have been charged with choosing a city for the convention that has the least expensive hotel rooms. you have narrowed your choices to Atlanta and Houston that are consistent with the results reported by Smith travel research. Because considerable historical data on the prices of the rooms in both cities are available the population standard deviations for the prices can be assumed to be $20 in Atlanta and $25 in Houston. Based on the sample data, can you conclude that the mean price of a hotel room in Atlanta is lower than the one in Houston.

Answer 1

No we can't make any such conclusion based on this information.

See, generally, in order to draw any conclusion or inference regarding population mean, we have to have some information regarding sample or population mean. But here we have information about standard deviations only, which tells nothing about corresponding population means.

For example, there can be two random variables X and Y where X~N(25,50) and Y~N(30,40).

See that the variance( and hence standard deviation) of X is more than that of Y, but the mean of Y is more than that of X. There can be many examples like this.

Here population standard deviations for the prices can be assumed to be $20 in Atlanta and $25 in Houston. But this information does not necessarily mean that the mean price of a hotel room in Atlanta is lower than the one in Houston. It can be lower or higher or same, anything. Only this piece of information is not enough to conclude about population mean.

If you have any further doubt, please say. I will try to answer it in comment section.

Hope the solution helps. Thank you.