Martin suspects that people carry less cash with them than they used to because of credit cards and other cashless payment systems. He decides to work on inventing a new system for people to use in place of cash that would be more user friendly and safe.

Martin conducted a survey to help convince investors to back the development of his new cashless system. One afternoon at the local mall, Martin surveyed a random sample of 95 people and asked the question, How much cash are you carrying in your wallet? The mean of his data is $8.00 with a standard deviation of $2.50. Assume the data is normally distributed. Based on this information, answer the following questions.

Part A: Now, Martin can reasonably guess that the standard deviation for the entire population of people at the mall during the time of the survey is $1.50. What is the 95% confidence interval about the sample mean? Interpret what this means in the context of the situation where 95 people were surveyed and the sample mean is $8. Use the information in this resource to help construct the confidence interval.

Part B: Would the interval found in part C increase, decrease, or remain the same if the confidence level desired were 99%? State your reasoning.

Part C: Would the interval found in part C increase, decrease, or remain the same if fewer than 95 people were surveyed? Justify your answer.