The manufacturer of an over-the-counter heartburn relief mediation claims that i
ID: 3182201 • Letter: T
Question
The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Test the hypotheses at a significance level =.05 using the critical value approach.
Explanation / Answer
Given that,
population mean(u)=3.5
standard deviation, =1.1
sample mean, x =3.3
number (n)=50
null, Ho: =3.5
alternate, H1: <3.5
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.3-3.5/(1.1/sqrt(50)
zo = -1.28565
| zo | = 1.28565
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.28565 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : left tail - ha : ( p < -1.28565 ) = 0.09928
hence value of p0.05 < 0.09928, here we do not reject Ho
ANSWERS
---------------
null, Ho: >3.5
alternate, H1: <3.5
test statistic: -1.28565
critical value: -1.645
decision: do not reject Ho
p-value: 0.09928
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