An aspirin manufacturer tills bottles by weight rather than by count. Since each

Question

An aspirin manufacturer tills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grams. Each of 100 tablets taken from a very largo lot is weighed, resulting in a sample average weight per tablet of 4.87 grams and a sample standard deviation of .35 grams. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test the appropriate hypotheses using a alpha = .01. Also, provide some bounds for the p-value resulting from this test using the appropriate statistical table (they are in the back of your textbook).

Explanation / Answer

Given that,
population mean(u)=5
sample mean, x =4.87
standard deviation, s =0.35
number (n)=100
null, Ho: =5
alternate, H1: !=5
level of significance, = 0.01
from standard normal table, two tailed t /2 =2.626
since our test is two-tailed
reject Ho, if to < -2.626 OR if to > 2.626
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4.87-5/(0.35/sqrt(100))
to =-3.714
| to | =3.714
critical value
the value of |t | with n-1 = 99 d.f is 2.626
we got |to| =3.714 & | t | =2.626
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -3.7143 ) = 0.0003
hence value of p0.01 > 0.0003,here we reject Ho
ANSWERS
---------------
null, Ho: =5
alternate, H1: !=5
test statistic: -3.714
critical value: -2.626 , 2.626
decision: reject Ho
p-value: 0.0003

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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