Question

1. Jake samples 14 customers at random and poling them on how much they would pay per hour to rent out Elsa for their event.  The results of his survey are below: $35    $51   $70   $65   $78   $68   $55  $61   $75    $50   $120   $90  $79  $97

Elsa is unsure how much she should charge people. She originally planned to charge more than $50 per hour for an appearance but is not sure if customers will feel this is too much. Find a 95% confidence interval for the true mean amount of money customers would spend on renting her services.  Assume it is a normal distribution.  If it is appropriate to find this interval, show all your work (provide the calculations for calculating the margin of error E using the formula), interpret the interval, and provide guidance to the owner about whether or not it would be appropriate to charge more than $50 per hour.  

b. Next, assume the margin of error to goes down to $10. How many more customers will he need to sample? assume that σ = $21.7.

c. If she only has $200 to spend on sampling, can he afford to be 99% confident that his interval is within $10 of the true mean? Assume the same standard deviation above and assume it costs $5 to sample each customer.  If he can afford the sample how much is the surplus?  If he cannot afford the sample, how much does he need?

Answer 1