Researchers were curious about the size of the bill at a restaurant based on whether a credit card was used to pay versus cash. The researchers took random samples of bills at restaurants across the US, and these sample statistics are summarized in the table below.

Method	Sample Size	Mean	Std. Dev.
Credit Card	51	29.4	14.5
Cash	106	19.5	9.4

a. Does this sample meet the conditions for the Central Limit Theorem to use a t-distribution? Explain why or why not.

b. Is there evidence of a difference in the mean size of the restaurant bill depending on the method of payment? Do the appropriate statistical analysis (confidence interval or hypothesis test) and show all steps involved in answering this question.

c. Can the researchers generalize the results of this study to all restaurants across the US? Explain why or why not.