Problem 6. Remaining time: 176:00 (min:sec) (3 points) A couple is interested in estimating the average cost of their weekly groceries. They take a sample of 30 weeks of grocery receipts and find that the average amount spent is a = $131.25 with a sample standard deviation of s = $11. Assume the amount spent per week is normally distributed. Use this information to answer the questions below. a. Compute a 95% confidence interval for A, the average cost of the couples' weekly groceries. Enter your smaller bound as the 'lower bound' and your larger bound as the 'upper bound.' Round your answers to at least five decimals if necessary Lower bound: $ Upper bound: $ b. Interpret the interval that you calculated in part a. We are % confident that the average cost of ? vis ? the upper and lower bounds of the interval. c. Suppose we were to increase the confidence level from 95% to 97% and compute a new confidence interval. If all other values/quantities stayed the same, how would the width of this new interval compare to the width of the interval computed in part a.? O A. The new interval would be narrower O B. The new interval would be the same width O C. The new interval would be wider O D. There is not enough information provided to determine how this would affect the interval width