Question

Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations s1=0.010 liter and s2=0.015 liter, respectively. A random sample of n1=25 bottles from machine 1 and n2=20 bottles from machine 2 results in average net contents of x1=2.04 liters and x2=2.07 liters.

(a) Test the hypothesis that both machines fill to the same net contents, using alpha=.05. What are your conclusions?

(b) Find the P-value for this test.

(c) Construct a 95% confidence interval on the difference in mean fill volume.

Answer 1

(a)
H0: Null Hypothesis: ( both machines fill to the same net contents ) (claim)

HA: Alternative Hypothesis: ( both machines do not fill to the same net contents ) (claim)

n1 = 25

1 = 2.04

s1 = 0.010

n2 = 20

2 = 2.07

s2 = 0.015

Pooled standard deviation (s_P) is given by:

Test Statistic is given by:
t = (2.04 - 2.07)/0.00375

= - 8.00

= 0.05

ndf = n1 + n2 - 2 = 25 + 20 - 2 = 43

From Table, critical values of t = 2.0167

Since calculated value of t = - 8.00 is less than critical value of t = - 2.0167, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that both machines fill to the same net contents.

(b)

By Technology, P - value = 0.0000

(c)

Confidence interval:

(2.04 - 2.07) (2.0167 X 0.00375)

= - 0.03 0.0076

= ( - 0.0376 ,- 0.0224)

Confidence Interval:

- 0.0376 < <   - 0.0224