What is the \"t\" statistic? What is our critical cutoff value for \"t\"? Should
ID: 2936602 • Letter: W
Question
What is the "t" statistic?
What is our critical cutoff value for "t"?
Should we reject or fail to reject the null hypothesis?
Scenario:
The Name-Letter effect is a phenomenon where people prefer the letters in their name more than letters that aren’t in their name. Nelson (2007) suggested that this effect might influence academic performance. Students whose names start with an A or B might perform better than students whose names start with a D or F. We want to test this using scores that have been separated into two groups.
students whose first or last name starts with A or B
students whose first or last name starts with C, D, or F
AB CDF 65.85 85.37 60.98 90.00 97.56 85.37 82.93 80.24 92.68 95.12 78.05 90.24 85.37 87.80 92.68 87.80 80.49 85.37 87.56 75.61 85.12 75.61 90.24 75.37 90.24Explanation / Answer
Given that,
sample1 data:(65.85 60.98 97.56 82.93 92.68 78.05 85.37 92.68 80.49 87.56 85.12 75.61 90.24 75.37 90.24 )
calucalated mean(x)=82.7153
caluclated standard deviation , s.d1=10.2
number(n1)=15
sample2 data:
(85.37 90 85.37 80.24 95.12 90.24 87.8 87.8 85.37 75.61 )
calucalated y(mean)=86.292
caluclated standard deviation, s.d2 =5.4273
number(n2)=10
null, Ho: u1 > u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.833
since our test is left-tailed
reject Ho, if to < -1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =82.7153-86.292/sqrt((104.04/15)+(29.45559/10))
to =-1.138
| to | =1.138
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 1.833
we got |to| = 1.13781 & | t | = 1.833
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:left tail - Ha : ( p < -1.1378 ) = 0.14229
hence value of p0.05 < 0.14229,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 > u2
alternate, H1: u1 < u2
test statistic: -1.138
critical value: -1.833
decision: do not reject Ho
p-value: 0.14229
we dont have evidence that Students whose names start with an A or B might perform better than students whose names start with a D or F
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