The following data are the amounts that a sample of 15 customers spent for lunch ($) at a fast-food restaurant. Complete parts (a) through (d) below. 7.47 6.29 5.79 6.51 8.32 9.50 7.08 6.82 5.90 4.87 6.47 5.52 7.86 8.36 9.63 a. Construct a 95% confidence interval estimate for the population mean amount spent for lunch ($) at a fast-food restaurant. SHS (Round to two decimal places as needed. Do not include the $ symbol in your answer.) b. Interpret the interval constructed in (a). Choose the correct answer below. A. Conclude with 95% confidence that the mean amount in dollars spent for lunch at the fast-food restaurant for the sample is contained in the interval. O B. 95% of the sample data fall between the limits of this confidence interval. O C. Conclude with 95% confidence that the population mean amount in dollars spent for lunch at the fast-food restaurant is contained in the interval. O D. The mean amounts in dollars spent for lunch at the fast-food restaurant of 95% of all samples of the same size are contained in the interval. c. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)? O A. The population distribution is normally distributed. O B. The population distribution is skewed left. O C. The population distribution is uniformly distributed. D. The population distribution is skewed right. d. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain. The assumption is for n = since