Question

8. A nutrition store in the mall is selling “Memory Booster,” which is a concoction of herbs and minerals that is intended to improve memory performance, but there is no good reason to think it couldn't possibly do the opposite. To test the effectiveness of the herbal mix, a researcher obtains a sample of 8 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of μ = 7. (Set the significance level ➔ a = .05)

Answer 1

8.

Assumed data,
sample mean, x =6
standard deviation, s =0.3, because not given in the data.
Given that,
population mean(u)=7
number (n)=8
null, Ho: μ=7
alternate, H1: μ!=7
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.365
since our test is two-tailed
reject Ho, if to < -2.365 OR if to > 2.365
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6-7/(0.3/sqrt(8))
to =-9.4281
| to | =9.4281
critical value
the value of |t α| with n-1 = 7 d.f is 2.365
we got |to| =9.4281 & | t α | =2.365
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -9.4281 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: μ=7
alternate, H1: μ!=7
test statistic: -9.4281
critical value: -2.365 , 2.365
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that population mean is 7.