Question

Historically a soft drink bottle contains 2 liters. A recent article complains that bottles actually contain less than 2 liters. To verify this claim a sample of 49 bottles is taken. The sample average is 1.976 liters with the sample standard deviation of 0.12 liters. Based on this sample, is there enough evidence to prove the claim that bottles actually contain less than 2 liters at 5% significance level?

(a) Yes

(b) No

(c) We don’t have enough information to decide

Answer 1

H0: = 2

Ha: < 2

Test statistics

t = ( - ) / (S / sqrt(n) )

= ( 1.976 - 2) / (0.12 / sqrt(49) )

= -1.4

df = n - 1 = 49 - 1 = 48

From T table,

t critical value at 0.05 significance level with 48 df = -1.677

Since test statistics > -1.677 , Do not reject H0.

We conclude that, we fail to support the claim that bottles actually contain less than 2 liters.

No