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 at least $375 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 110 motorcycle enthusiasts, all of whom resemble Jacobi's usual clientele, and determine that the average amount people are willing to pay is $395, with a standard deviation of $41.

Using this information, you conduct a hypothesis test at a 5% level of significance to check whether Jacobi's belief is justified and to help him decide whether to stock this product.