Question

The fill weight of tomato paste in seven cans tested were: 7.2, 6.8, 6.7, 7.3, 6.9, 6.8 and 7.0 ounces. Suppose the manufacturer requires a standard deviation of less than 0.12. Does the data indicate that the standard deviation is less than 0.12 ounce? Test using α = 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.12
Alternative Hypothesis, Ha: σ < 0.12

Rejection Region
This is left tailed test, for α = 0.05 and df = 6
Critical value of Χ^2 is 1.635
Hence reject H0 if Χ^2 < 1.635

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (7 - 1)*0.2225^2/0.12^2
Χ^2 = 20.628

P-value Approach
P-value = 0.9979
As P-value >= 0.05, fail to reject null hypothesis.