Question

The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are:

Edne: 10, 13, 12, 11, 14 and 12
Orno: 13, 15, 12, 16, 14, 17, 19 and 14

Testing the claim at the 0.005 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value? Assume equal standard deviations for both samples.

a.) 3.372

b.) 3.428

c.) 3.012

d.) 3.055

Answer 1

Given

H0 : ₁ = ₂

H1 : ₁ < ₂

n1 = 6

x1 = 12

s1² = 2 (Formula for S below)

n2 = 8

x2 = 15

s2² = 5.143

The test statistic is

t=(xbar1-xbar2)/sqr(s1^2/n1+s2^2/n2)

=(12-15)/sqrt(2/6 +5.143/8)

= -3.036

t-critical = -3.055 (Left -tailed test)

t value > t-critical

Failed to Reject H0.