Question

Automated filling machine is used to fill bottles with liquid detergent. A random sample of 25 bottles results in a sample variance of fill volume of s2 = 0.0102 (fluid ounces)2 . If the variance of fill volume exceeds 0.01 (fluid ounces)2 , an unacceptable proportion of bottles will be underfilled or overfilled.

a) Is there evidence in the sample data to suggest that the manufacturer has a problem with underfilled or overfilled bottles? Use α = 0.05, and assume that fill volume has a normal distribution.

b) Find P-Value and compare it with the result in part (a).

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.01
Alternative Hypothesis, Ha: σ^2 ≠ 0.01

Rejection Region
This is two tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 are 12.401 and 39.364
Hence reject H0 if Χ^2 < 12.401 or Χ^2 > 39.364

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*0.0102/0.01
Χ^2 = 24.48

fail to reject null hypothesis.

b)

P-value Approach
P-value = 0.8689
As P-value >= 0.05, fail to reject null hypothesis.