Samsung is trying to decide whether to produce an upgrade of one of its cell phone software. Customers would have to pay $95 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 25% of their customers. The company will survey a random sample of 50 customers about this issue Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.
In the company's survey, 14 customers are willing to pay $95 each for the upgrade. Do the sample data give convincing evidence that more than 25% of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the α=0.05 significance level.