1. (8+4=12 points ) A grocery store claims that the mean waiting time for their customers is less than 4.5 minutes before being served by the cashier. An agency wanted to test their claim and they recorded the waiting times of a random sample of 45 customers. The sample mean and the sample SD were found to be 4.64, and 0.82 minutes, respectively. a) Do these data support the store's claim? Test using =0.05. Clearly state i) the parameter of interest, ii) the null and the alternative hypotheses, iii) kind of test you used with justification and iv) your conclusion. b) Suppose they want to estimate the true mean waiting time with a margin of error of no more than 0.1 minutes. How big a sample do they need? Use 95% confidence level. Choose the best option. a) 17 b) 182 c) 258.31 d) 258 e) 259