Question

3. 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, 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 a = 0.01.
b. Construct a 95% two-sided confidence interval on the mean fill volume.
c. Does the assumption of normality seem appropriate for the fill volume data?
d. Repeat (a,b,c) above for a = 0.05. Compare with results for a = 0.01.

Answer 1

a) = 0.01

From given data we have

mean = 12.015

Sample std deviation = 0.03027

(Right tailed test)

Mean difference /std error = test statistic

p-value = 0.0582

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.

b)

c) Yes

d)

= 0.05

From given data we have

mean = 12.015

Sample std deviation = 0.03027

(Right tailed test)

Mean difference /std error = test statistic

therefore we fail to reject the hypothesis that μ>12

Conclusion:

This means that the probability that the mean net content exceeds 12 is good

option b and c will be same for = 0.05