SOLUTION: A machine is set to ﬁll a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed an average of 8.8 grams and a standard deviation of 0.23 grams. (a) Compute

Question 1155919: A machine is set to ﬁll a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed an average of 8.8 grams and a standard deviation of 0.23 grams.
(a) Compute the 95% conﬁdence interval for the population mean µ.
(b) At 1% signiﬁcance level, should we conclude that the mean weight is below 9.0 grams?
Specify your H0 and H1, the test you use, and your conclusions.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: Weight is 9.0 gm or above
Ha: Weight is below 9.0 gm
alpha=0.01 P{reject Ho|Ho true}
test statistic is a t df=7 0.995
critical value t<3.499
calculation t=(8.8-9)/0.23/sqrt(8)
=-0.2*sqrt(8)/0.23=-2.45. Fail to reject Ho.
Conclude that at the 1% level that there is insufficient evidence to say that the filling is not 9.0 gm. (p-value=0.022)
RELATED QUESTIONS
2. A Corkill Machine is set ti fill a small bottle with 9.0 grams of medicine. It is... (answered by CPhill)

This is not out of a book this is homework - any help is greatly appreciated. A... (answered by stanbon)

3. The net weight of a sample bottles filled by a machine manufactured by Edne, and the... (answered by CPhill)

A machine is set to fill the small size packages of M&M candies with 56 candies per bag.... (answered by vleith)

A machine is set to fill the small size packages of M&M candies with 56 candies per bag.... (answered by stanbon)

A machine is set to fill the small size packages of M&M candies with 56 candies per bag.... (answered by Brownjewel)

A machine is set to fill the small size packages of M&M candies with 56 candies per bag.... (answered by Boreal)

A manufacturer of salad dressings uses machines to dispense liquid ingredients into... (answered by ikleyn)

A manufacturer of salad dressings uses machines to dispense liquid ingredients into... (answered by CPhill)