An automated filling machine is used to fill bottles with liquid detergent. A ra

Question

An automated filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s^2 = 0.0153 (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 alpha = 0.01, and assume that fill volume has a normal distribution. b) Suppose, you stated your alternative hypothesis incorrectly as sigma^2

Explanation / Answer

Solution:

a. Null Hypothesis (Ho): ^2 = 0.01

Alternative Hypothesis (Ha): ^2 > 0.01

Test Statistics

X^2 = (n – 1)s^2/^2

X^2 = (20 – 1) (0.0153)/0.01

X^2 = 29.07

Degrees of freedom, df = n -1 = 20 – 1 = 19

Using chi-square tables, the critical value at a = 0.05 and df = 19 is

X^2 (0.05, 19) = 30.14

Since test statistics is less than the critical value, we fail to reject Ho.

b. If hypothesis is incorrectly stated as left-tailed, the critical value would be lower and decision would be to reject Ho.

c. If hypothesis in part a holds true, the variance volume would not exceed (0.01 fluid ounces)^2. If hypothesis in part b holds true, the variance volume would exceed (0.01 fluid ounces)^2.  

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