Question

You are thinking about opening a restaurant and are searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. Describe a Type I and a Type II error, and explain the consequences of each

Answer 1

The type I error and type II error can be described as follows:

Type I error: We can conclude that if the mean exceeds $85000, when in fact it does not. Thus, opening your restaurant in a locale that will not support it).

Type II error: We can conclude that if the mean income does not exceed $85000, when in fact it does. Thus, deciding not to open your restaurant in a locale that will support it.

What is a Type I and a Type II error?

A Type I error in statistics is described as rejecting the null hypothesis when it is actually true, and a Type II error is defined as failing to reject the null hypothesis when it is genuinely untrue.

The type I error and type II error can be described as follows:

• Type I error: We can conclude that if the mean exceeds $85000, when in fact it does not.
• Type II error: We can conclude that if the mean income does not exceed $85000, when in fact it does.

The consequences of each error are:

If you launched your business in an inappropriate location, you would incur a financial loss before realizing your error.

If you do not open your restaurant in an ideal location, you will miss out on the potential to make a profit, but you will not necessarily lose money.

Learn more about type I error and type II error here:

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