Two new mathematics learning techniques are being tested. The researchers are un
ID: 3318690 • Letter: T
Question
Two new mathematics learning techniques are being tested. The researchers are unsure which one, if any, will be better. Two hundred students were randomly selected from a population. Ninety of them were randomly assigned to use Technique A, and 110 of them were randomly assigned to use Technique B. Each student spent 30 minutes learning the technique to which they were assigned, and then were asked to complete a task. The time to complete the task was recorded, in seconds. A shorter time indicates better mastery of the task. The data are below:
Technique A: sample average = 26.1, sample SD = 7.2
Technique B: sample average = 27.9, sample SD = 12.4
(a) State hypotheses relevant to the research question.
(b) Perform a test of the hypotheses from (a) using a signi cance level of 10%. Make sure to compute the
test statistic and P-value, and make a conclusion in context
Explanation / Answer
Given that,
mean(x)=26.1
standard deviation , s.d1=7.2
number(n1)=90
y(mean)=27.9
standard deviation, s.d2 =12.4
number(n2)=110
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.1
from standard normal table, two tailed t /2 =1.662
since our test is two-tailed
reject Ho, if to < -1.662 OR if to > 1.662
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =26.1-27.9/sqrt((51.84/90)+(153.76/110))
to =-1.2812
| to | =1.2812
critical value
the value of |t | with min (n1-1, n2-1) i.e 89 d.f is 1.662
we got |to| = 1.28121 & | t | = 1.662
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.2812 ) = 0.203
hence value of p0.1 < 0.203,here we do not reject Ho
ANSWERS
---------------
(a).
null, Ho: u1 = u2
alternate, H1: u1 != u2
(b).
test statistic: -1.2812
critical value: -1.662 , 1.662
decision: do not reject Ho
p-value: 0.203
we don't have sufficient evidence to support the claim.
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