A company that makes cola drinks states that the mean caffeine content per 12-ou

Question

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim, During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 41.5 milligrams. Assume the population is normally distributed and the population standard deviation is 6.7 milligrams. At alpha = 0.06, can you reject the company's claim? Complete parts (a) through (e) Find the standardized test statistic, Z = (Round to two decimal places as needed) Decide whether to reject or fail to reject the null hypothesis. Since z is in the rejection region, fail to reject the null hypothesis. Since z is not in the rejection region, fail to reject the null hypothesis. Since z is not in the rejection region, reject the null hypothesis Since z is in the rejection region, reject the null hypothesis. Interpret the decision in the context of the original clam At the 6% significance level, there ___________ enough evidence to _____________ the company's claim that the mean caffeine content per 12-ounce bottle of cola _____________ milligrams

Explanation / Answer

Given that,
population mean(u)=40
standard deviation, =6.7
sample mean, x =41.5
number (n)=30
null, Ho: =40
alternate, H1: !=40
level of significance, = 0.06
from standard normal table, two tailed z /2 =1.881
since our test is two-tailed
reject Ho, if zo < -1.881 OR if zo > 1.881
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 41.5-40/(6.7/sqrt(30)
zo = 1.22624
| zo | = 1.22624
critical value
the value of |z | at los 6% is 1.881
we got |zo| =1.22624 & | z | = 1.881
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.22624 ) = 0.22011
hence value of p0.06 < 0.22011, here we do not reject Ho
ANSWERS
---------------
null, Ho: =40
alternate, H1: !=40
test statistic: 1.22624
critical value: -1.881 , 1.881
decision: since z is not in the rejection region, fail to reject Ho
p-value: 0.22011
is not evidence

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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