Question

A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.
(a) Suppose that the manufacturer wants to be sure that the mean net contents exceeds 12 oz. What conclusions can be drawn from the data (use α= 0.01).

(b) Construct a 95% two-sided confidence interval on the mean fill volume.

Answer 1

Answer:

There is no statistical evidence at 1% level to accept that    the mean net contents exceeds 12 oz.

Step-by-step explanation:

Given that a random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.

We find mean = 11.015

Sample std deviation = 3.157

a) $H_0: \bar x= 12 oz\\H_a: \bar x >12$

(Right tailed test)

Mean difference /std error = test statistic

$\frac{11.015-12}{\frac{3.157}{\sqrt{10} } } \\=-0.99$

p value =0.174

Since p >0.01, our alpha, fail to reject H0

Conclusion:

There is no statistical evidence at 1% level to accept that    the mean net contents exceeds 12 oz.