{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Statistics Ch 7 Quiz 3 of 4

Statistics Ch 7 Quiz 3 of 4 - size of the sample is not a...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: size of the sample is not a matter at issue here since all requirements for use of the Student t have been met. 3. This real example is very similar to one that was performed in in-patient pharmacy at Tripler several years ago. So, here goes: The Medassist Pharmaceutical Company uses a machine to pour cold medicine into bottles in such a way that the standard deviation of the weights is 0.15 oz. A new machine is tested on '1’] bottles, and the standard deviation for this sample is 0.12 oz. The Dayton Machine Company, which manufactures the new machine, claims that it ﬁlls bottles with lower variation. At the 0.05 signiﬁcance level, test the claim made by the Dayton Machine Company. If Dayton’s machine is being used on a trial basis, should its purchase be considered? Solution: Here we want to test variances, so we must use the Chi-squared statistic and the Chi-squared distribution. a. The claim is that the Dayton machine has a fill variance less than 0.15, so the counter claim is that the Dayton machine has a fill variance of greater than or equal to 0.15. The null hypothesis is then H0 :0“ = 0.15. The alternative hypothesis comes in this case from the original claim (the other has the equality) so HI :0' < 0.15 . The hypothesis shows we need a left sided one tail test. The distribution for variances is the Chi-squared distribution. The dof is one less than the sample size or 70. 2 2 The Chi square statistic is given by 12 = ("—1215— = (19(0—122) or (0.15) For 70 degrees of freedom, and using the Chi-Square table for a 5% level of signiﬁcance we have a bit of a problem- While the normal and the Student t are symmetric, the Chi-square is not, and the table values are read from the right, not the left. So since we want a left handed test, we much leave 95% of the area to the right of the critical value. We look up the value, then for 95%, not 5%: This critical value is 51.739. Now since 44.8 is to the left of 5 1 .739, our test statistic is in the rejection area. Hence we reject the null and accept the alternative: they do better than a standard deviation of less than 0.15. So this supports the procurement of the new machine. = 44.3 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern