Using the data provided, determine if clients are willing to pay more than $26$ per cake with a $95\%$ confidence interval. Determine also if that remains true if charging more than $30$ per cake. Perform a Cohen$$s d test to further understand the difference between the means of the price data $($see the sheet named $$Part $3$ Revenues$)$ and the survey data $($see the sheet named $$Part $3$ Survey$).$

$(15$ marks$)$

Part $3$b

Discuss the results of your analysis considering the different outcomes, and present them in a form suitable for a business audience. Include a discussion on the risk of Type II errors in this analysis.