Question: Bumble is back serving as a waiter at another restaurant, where it is known from past experiences that one in four customers would supposedly leave over 18% gratuity. Bumble served 100 customers today but only 14 of them tipped him over 18%. Still confident in his service, Bumble said he just had another bad day.
- What is the known population proportion of getting the high tip amount of 18% or more for the waiters at this restaurant?
- What is Bumble's sample proportion of getting the high tip this day?
- Assuming that Bumble's customers represent a simple random sample of those who could have dined there, for simple random samples of n = 100, what is the probability of only 14 or fewer people giving him over 18% gratuity? Also comment on his claim of just having a bad day.
Based on the above sample observation, please construct the 95% confidence interval for Bumble's true rate of getting the high tip of 18% or more. Please interpret the answer as well.