10 You are opening up an upscale ice cream shop in town, and before you open, you decide to do some market research. You sample 11 individuals and ask each one "How much would you pay for a cup of high-quality ice cream?" Your results from the survey are as follows: $2.78, $3.16, $3.10, $2.37, $3.58, $3.31, $3.37, $4.31, $2.69, $2.31, $3.82 Let u denote the amount an individual in town will pay for a cup of high-quality ice cream on average. Assume that prices that people are willing to pay are normally distributed. We will be constructing a 95% confidence interval for u. a. (3pts) What is the sample mean of the prices? Round answers to 2 decimal points. Do not include dollar signs ($) in your answer Sample mean: $ b. (2pts) The computation of the 95% confidence interval requires finding a quantile from a t-distribution with how many degrees of freedom? Degrees of freedom: c. (3pts) What is the standard error of the sample mean? Round answers to 2 decimal points. Do not include dollar signs ($) in your answer Standard error: $ d. (4pts) Compute the 95% confidence interval for the sample mean . Round answers to 2 decimal points. Do not include dollar signs ($) in your answer to : e. (2pts) What is the margin of error of the confidence interval? Round answers to 2 decimal points. Do not include dollar signs ($) in your answer f. (2pts) Which of the following will decrease the width of the confidence interval? Increase the standard deviation Increase the confidence level Increase the sample size All of the above