Question

1. An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design.

At the start of each session, no subject reported being “high.” After smoking the cigarette, participants rated how “high” they felt, using a positive continuous scale (0 representing not at all “high”). For the placebo condition, participants reported a mean “high” feeling of 11.3, with a standard deviation of 15.5. Is there evidence of a significant placebo effect, with subject feeling significantly “high” after smoking a placebo marijuana cigarette?

the appropriate null and alternative hypotheses for this study- H₀: m = 0 versus H_a: m > 0

a. What is the appropriate statistic to test this hypothesis? What is its value?

b. what is the P-value for the appropriate test? Specify the distribution used and all relevant parameters.

Answer 1

Given that,
population mean(u)=0
sample mean, x =11.3
standard deviation, s =15.5
number (n)=18
null, Ho: μ=0
alternate, H1: μ>0
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.74
since our test is right-tailed
reject Ho, if to > 1.74
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.3-0/(15.5/sqrt(18))
to =3.093
| to | =3.093
critical value
the value of |t α| with n-1 = 17 d.f is 1.74
we got |to| =3.093 & | t α | =1.74
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 3.093 ) = 0.0033
hence value of p0.05 > 0.0033,here we reject Ho
ANSWERS
---------------
null, Ho: μ=0
alternate, H1: μ>0
a.
the appropriate statistic to test this hypothesis is t test for single mean with known sample standard deviation.
test statistic: 3.093
critical value: 1.74
decision: reject Ho
b.
p-value: 0.0033
we have enough evidence to support the claim that significant placebo effect, with subject feeling significantly “high” after smoking a placebo marijuana cigarette.