Maine Coons are the largest breed of domestic cat. Suppose the average healthy body weight of adult males of this breed is 18lb. One veterinarian suspects that a popular brand of cat food is more fattening than normal, and wants to be able to discourage owners of her patients from using that brand. She collects data on 10 healthy patients (adult male Maine coon cats) that present at her clinic for an annual exam that also eat this brand of cat food, and obtains the following data on their weight rounded to the closest integer (in lbs):
17 23 15 21 28 26 18 22 24 18
If the weight distribution is known to be normally distributed, do the data support the veterinarian's suspicion? Conduct a hypothesis test at the 5% significance level. Define your parameter (μ), state your hypotheses, conduct the test and write a conclusion.