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 decides to carry out a test of hypothesis. The null hypothesis is given by 0:=13.50 .
The hypothesis test is set up to provide the marketing manager with:

proof that the null hypothesis is true.

evidence in favor of the null hypothesis.

evidence against the null hypothesis in favor of the alternative.

evidence against the alternative hypothesis in favor of the null hypothesis.