In: Statistics and Probability
During the investigation of an alleged unfair trade practice, the Federal Trade Commission takes a random sample of 50 “3-ounce” candy bars from a large shipment. If the mean and the standard deviation of their weights are, respectively, 2.92 ounces and 0.21 ounce, determine at the level of 0.01 significance whether the commission has grounds upon which to proceed against the manufacturer on the unfair practice of short-weight selling. State hypotheses, P-value, and conclusion.
Ho : µ = 3
Ha : µ < 3
(Left tail test)
Level of Significance , α =
0.010
sample std dev , s = 0.2100
Sample Size , n = 50
Sample Mean, x̅ = 2.9200
degree of freedom= DF=n-1= 49
Standard Error , SE = s/√n = 0.2100 / √
50 = 0.0297
t-test statistic= (x̅ - µ )/SE = ( 2.920
- 3 ) / 0.0297
= -2.694
critical t value, t* =
-2.405 [Excel formula =t.inv(α/no. of tails,df)
]
p-Value =
0.0048 [Excel formula =t.dist(t-stat,df)
]
Decision: p-value<α, Reject null hypothesis
Conclusion: There is enough evidence to conclude
that commission has grounds upon which to proceed against
the manufacturer on the unfair practice of short-weight selling