The following are reaction time results for catching an object, with the dominant hand, that is...

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

Set up null and alternative hypothesis test:
Show all steps, (whether from Excel, StatCrunch, or TI-84 +) used.
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?

Expert Solution

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.

orchestra answered 1 year ago

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