Question

Suppose that the owner of a fast food restaurant recently purchased a new soft drink machine, designed to dispense 16 oz for a small beverage. The actual amount dispensed is normally distributed and should have a mean of 16 oz, but the manager suspects that the machine may be underfilling the cups. He selects a random sample of 7 small soft drinks, as filled by the machine. The volumes dispensed into each cup, in ounces, are listed below. 15.7,15.8,15.6,16.1,16.0,15.7,15.5

Answer 1

Explanation:

Let X be amount dispensed

X is N(16, sigma)

`H_0: Mean =16\\H_a : Mean <16`

(One tailed test)

Count, N: 7

Sum, Σx: 110.4

Mean, μ: 15.771428571429

Variance, s^2 0.039183673469388

s=0.1979

Test statistic = Mean diff/std error where std error = s/sqrt n

=-2.828

p value = 0.01501

p <0.05

Hence we conclude that the manager suspects that the machine may be under filling the cups is confirmed and evident statistically