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 𝜎=$3.50 . To address the CEO’s conjecture, the
marketing manager carried out a hypothesis test of 𝐻0:𝜇=13.50 vs.
𝐻𝛼:𝜇>13.50 and obtained a 𝑃 ‑value = 0.077. To illustrate his
results, the director also wanted to calculate a 95% confidence
interval with a margin of error 𝑚= $1.00.
The required sample size equals?: 48. 100. 25. 30.