Adata set about speed dating includes "like" ratings of male dates made by the female dates. the summary statistics are nequals187, x overbarequals7.57, sequals1.85. use a 0.01 significance level to test the claim that the population mean of such ratings is less than 8.00. assume that a simple random sample has been selected. identify the null and alternative hypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim.

Naruto is choosing between two venues that will deliver food to his house. with probability 1/3 he will choose ramen mania (r), and with probability 2/3 he will choose sushi (s). if he chooses r, 15 minutes after making the call, the remaining time it takes the food to arrive is exponentially distributed with average 10 minutes. if he orders s, 10 minutes after making the call, the time it takes the food to arrive is exponentially distributed with an average of 12 minutes. given that he has already waited 25 minutes after calling, and the food has not arrived, what is the probability that he ordered from r? i am really stuck on how to set this up, so if you could be extra clear, that would be super ! in advance