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)

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a right-tailed test, so the critical-value is given by:

Since the test statistic value is less than the critical value, so we do not have sufficient evidence to reject H0.

b)

Since this is a right-tailed test, so the p-value is given by:

Since p-value is greater than 0.05, so we do not have sufficient evidence to reject the null hypothesis H0.

Hence the result is same as that in part (a).