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

Question

An automatic 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 s2 = 0.0153 square fluid ounces. If the variance of fill volume exceeds 0.01 square fluid ounces, an unacceptable proportion of bottles will be under or overfilled. Is there evidence in the sample data to suggest that the manufacturer has a problem with under and overfilled bottles? Use = 0.05, and assume that fill volume has a normal distribution.

Parameter:

Null Hypothesis:

Alternative:

Test Statistic:

Reject Region:

Calculation:

Decision:

P-value:

Explanation / Answer

The parameter of interest is the population variance s2.

Here we have to test the hypothesis that,

H0 : 2 = 0.01 Vs H1 : 2 > 0.01

where 2 is variance of population.

Given values are :

s2 = sample variance = 0.0153

n = number of bottles = 20

Alpha = level of significance = 0.05

The test statistic is,

X2 = (n-1) * s2 /  2

= (20-1)*0.0153 / 0.01

= 29.07

P-value we can find by using EXCEL.

syntax is,

=CHIDIST(x, deg_freedom)

where x is test statistic value.

deg_freedom = n-1 = 20-1 = 19

P-value = 0.06

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the variance of fill volume is 0.01.

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