Could any experts provide me with a detailed step-by-step solution to the follow
ID: 3228203 • Letter: C
Question
Could any experts provide me with a detailed step-by-step solution to the following problem using standard error statistics formulas:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or senior. The school randomly surveys 10 freshman and 10 seniors and asks them to rate how satisfied they are at the school on a scale 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. If freshman had a mean score of 6.7 and a standard deviation of 1.62, and seniors had a mean score of 5.9 and a standard deviation of 2.21, are the results signficant at the 0.05 level, why or why not?
Explanation / Answer
Given that,
mean(x)=6.7
standard deviation , s.d1=1.62
number(n1)=10
y(mean)=5.9
standard deviation, s.d2 =2.21
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.26
since our test is two-tailed
reject Ho, if to < -2.26 OR if to > 2.26
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =6.7-5.9/sqrt((2.6244/10)+(4.8841/10))
to =0.92
| to | =0.92
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 2.26
we got |to| = 0.92324 & | t | = 2.26
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.9232 ) = 0.38
hence value of p0.05 < 0.38,here we do not reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 0.92
critical value: -2.26 , 2.26
decision: do not reject Ho
p-value: 0.38
we have no evidence that results are signficant at the 0.05 level,