In the Math $110$ Estrada FA$22$ folder load the data set StatCrunchUFA$23.$ This is a random sample of $500$ students. The variable CC debt measures the dollar amount in credit card debt for each student.

a$.$ Use this data set to create a $95\%$ confidence interval to estimate the mean credit card debt amount for all students StatCrunchU.

b$.$ Interpret this interval in the context of the problem.

c$.$ What is one change we can make to the interval that will make the interval narrower? Show how your suggestion has the impact predicted.

d$.$ Based on the intervals you created, is it reasonable to assume the mean credit card debt amount for all StatCrunchU students is $$3000?$ Explain