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 x¯=$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 H0:=13.50 vs. H:>13.50 and obtained a P‑value = 0.017. At level of significance =0.05 , the null hypothesis is rejected. However, the marketing director later finds that, in fact, the average lunch price is not $13.50.
Which of the following is true:
a. Type I error was committed
b. Type II error was committed
c. No error was made