A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ¯=$14.50 . Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is =$3.50
. To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of 0:=13.50
vs. :>13.50
and obtained a
‑value =
0.077.
The study meets all conditions for inference:

if the customers constitute an SRS and the population distribution of lunch prices is Normal.

if the customers constitute an SRS and the variance is small.

if the population of lunch prices is Normal and the variance is known.

if the population of lunch prices is Normal and the sample is not too small.