Answer using the 6 step hypothesis testing process and giving working out.

With the extra profits generated from the new customers, Jacobi is considering expanding his product range. He is interested in stocking a new type of motorcycle headset camera. To fit with current business plans, the new product would have to generate a minimum of 37.5% margin to be worthwhile. With that in mind, he hypothesises that customers will be willing to pay more than $425 for this product, which is the minimum sale price for it to be viable at the specified margin.

To test if his belief is true, Jacobi hires a market researcher (you) to determine how much customers may be willing to pay for this product. You collect data from a sample of 250 motorcycle enthusiasts, all of whom resemble Jacobis usual clientele, and determine that the average amount people are willing to pay is $429, with a standard deviation of $28.

Using this information, you conduct a hypothesis test at a 5% level of significance to check whether Jacobis belief is justified and to help him decide whether to stock this product. In your answer, state clearly what process and evidence you are using from the data to support your suggestion