Testing Claims In Exercises 39-46, (a) write the claim mathematica identify Ho a

Question

Testing Claims In Exercises 39-46, (a) write the claim mathematica identify Ho and Ha (b) find the critical values and identify the rejection region c) find the standardized test statistic, (d) decide whether to reject or fail to rege 5 the null hypothesis, and (e) interpret the decision in the context of the originl claim. 39. Caffeine Content in Colas A company that makes cola drinks states tha the mean caffeine content per one 12-ounce bottle of cola is 40 milligram 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 milligrams with a standard deviation of 7?milligrams. At ? = 0.01, canyou 8 reiect the company's claim? (Adapted from American Beverage Association

Explanation / Answer

Given that,
population mean(u)=40
sample mean, x =39.2
standard deviation, s =7.5
number (n)=30
null, Ho: ?=40
alternate, H1: ?!=40
level of significance, ? = 0.01
from standard normal table, two tailed t ?/2 =2.756
since our test is two-tailed
reject Ho, if to < -2.756 OR if to > 2.756
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =39.2-40/(7.5/sqrt(30))
to =-0.5842
| to | =0.5842
critical value
the value of |t ?| with n-1 = 29 d.f is 2.756
we got |to| =0.5842 & | t ? | =2.756
make decision
hence value of |to | < | t ? | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -0.5842 ) = 0.5636
hence value of p0.01 < 0.5636,here we do not reject Ho
ANSWERS
---------------
null, Ho: ?=40
alternate, H1: ?!=40
test statistic: -0.5842
critical value: -2.756 , 2.756
decision: do not reject Ho
p-value: 0.5636

we have enough evidence that the mean caffeine content per one 12 ounce bottle of cola is 40 milligrams

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