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 38.3 milligrams. Assume the population is normally distributed and the population standard deviation is 6.5 milligrams. At alpha = 0.06. can you reject the company's claim? Complete parts (a) through (e). (a) Identify H_0 and H_a. Choose the correct answer below. A. H_0: mu = 38.3 H_a: mu notequalto 38.3 B. H_0: mu notequalto 38.3 H_a: mu = 38.3 C. H_0: mu = 40 H_a: mu notequalto 40 D. H_0: mu lessthanorequalto 40 H_a: mu > 40 E. H_0: mu lessthanorequalto 38.3 H_a: mu > 38.3 F. H_0: mu notequalto 40 H_a: H_a: mu = 40 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical value is B. The critical values are plusminus Click to select your answer(s).

Explanation / Answer

Given that,
population mean(u)=40
standard deviation, =6.5
sample mean, x =38.3
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 = 38.3-40/(6.5/sqrt(30)
zo = -1.43251
| zo | = 1.43251
critical value
the value of |z | at los 6% is 1.881
we got |zo| =1.43251 & | 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 != -1.43251 ) = 0.152
hence value of p0.06 < 0.152, here we do not reject Ho
ANSWERS
---------------
null, Ho: =40
alternate, H1: !=40
test statistic: -1.43251
critical value: -1.881 , 1.881
decision: do not reject Ho
p-value: 0.152

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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