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

Given that

The fill weight tomato paste in seven cans tested were: 7.2,6.8,6.7,7.3,6.9,6.8 and 7.0.

n = 7

From the sample data

= 6.96 , S = 0.2225

H0: = 0.12

Ha: < 0.12

Test statistics

= ( n - 1) S2 / 2

= ( 7 -1) * 0.22252 / 0.122

= 20.63

Chi-square critical value at 0.05 level with 6 df = 1.635

Since test statistics > 1.635 , Fail to reject H0.

We do not have sufficient evidence to conclude that the standard deviation is less than 0.12 ounce.