A machine is used to fill containers with a liquid product. Fill volume can be a

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) Construct and run an appropriate test of hypothesis in order that manufacturer can be sure that the mean net contents exceed 12 oz. What conclusions can be drawn from the data (use = 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? Why or why not?

Please show work

Explanation / Answer

Answer to part a)

the hypothesis are as shown below:

Null hypothesis: Average content is less than or equal to 12 oz.

Alternate hypothesis: Average content is more than 12 oz.

.

In order to test this hypothesis we need to find the mean and the sample standard deviation of the 10 observations

Mean (M) = 12.015

Standard deviation (s) = 0.0303

n = 10

.

Formula of test statistic is:

t = (12.015 - 12) / (0.0303/sqrt(10))

t = 1.5655

.

P value of t = 1.5655 at df = 10-1=9 would be :

[it is a one tailed test]

We get P value = 0.07595

.

Decision: since this p value is greater than 0.05 , we fail to reject the null

Conclusion: Thus we conclude that mean doesnot exceed 12 oz.

.

Answer to part b)

The formula of confidence interval is:

mean - t*s/root(n) , mean + t*s/root(n)

here t = critcal value for df = 9 and significance level = 0.01

T critical = 3.250

.

Thus we get the confidence intervals as follows:

12.015 - 3.250 * 0.0303 /sqrt(10) , 12.015 + 3.250 * 0.0303 / sqrt(10)

11.9839 , 12.04614

.

Answer to part c)

The assumption of normality doesnot seems to be appropriate since the sample size n is too small

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.