Question

The following are reaction time results for catching an object, with the dominant hand, that is dropped 2 feet above the hand. The two groups are A (the experimental group) and B (the control group). Experimental and Control groups are the same as listed at the beginning of the description of the study. Use the p-value approach, with a-level = .05.

N1: mean = .22 seconds; Standard Deviation = .034 seconds

N2: mean = .203 seconds; Standard Deviation = .041 seconds

1. Set up null and alternative hypothesis test:
2. Show all steps, (whether from Excel, StatCrunch, or TI-84 +) used.
3. Write out your conclusion. Is there sufficient statistical evidence to support the conclusion that the reaction time for Group A is greater than the reaction time for Group B?

Answer 1

Assume , sample sizes n1 =n2 =10 because not given in the data.
Given that,
mean(x)=0.22
standard deviation , s.d1=0.034
number(n1)=10
y(mean)=0.203
standard deviation, s.d2 =0.041
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =0.22-0.203/sqrt((0.00116/10)+(0.00168/10))
to =1.009
| to | =1.009
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 1.833
we got |to| = 1.0093 & | t α | = 1.833
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.0093 ) = 0.1696
hence value of p0.05 < 0.1696,here we do not reject Ho
ANSWERS
---------------
i.
null, Ho: u1 = u2
alternate, H1: u1 > u2
ii.
test statistic: 1.009
critical value: 1.833
decision: do not reject Ho
p-value: 0.1696
iii.
we do not have enough evidence to support the claim that the reaction time for Group A is greater than the reaction time for Group B.