A comparison of vanadium content was used to determine if two samples of crude o
ID: 2930020 • Letter: A
Question
A comparison of vanadium content was used to determine if two samples of crude oil came from the same source. For sample 1, four replicate determinations returned a mean vanadium concentration of 140 ppm with a standard deviation of ± 7 ppm. Eight replicate determinations of sample 2 returned a mean vanadium concentration of 159 ppm ± 6 ppm. Do these samples differ at the 95% confidence level? On your written work, be sure it is clear how you proved your answer statistically. O To a 95% confidence, the samples DO differ-based on a t test for samples with different standard deviations. O To a 95% confidence, the samples DO differ-based on a paired t test O To a 95% confidence, the samples DO NOT differ-based on a t test for samples with different standard deviations. O To a 95% confidence, the samples DO differ-based on a t test using spooled O To a 95% confidence, the samples DO NOT differ-based on a t test using spooled O To a 95% confidence, the samples DO NOT differ-based on a paired t test O To a 95% confidence, the samples DO differ-the confidence intervals do not overlap. O To a 95% confidence, the samples DO NOT differ-the confidence intervals overlap.Explanation / Answer
Given that,
mean(x)=140
standard deviation , s.d1=7
number(n1)=4
y(mean)=159
standard deviation, s.d2 =6
number(n2)=8
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =3.182
since our test is two-tailed
reject Ho, if to < -3.182 OR if to > 3.182
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =140-159/sqrt((49/4)+(36/8))
to =-4.642
| to | =4.642
critical value
the value of |t | with min (n1-1, n2-1) i.e 3 d.f is 3.182
we got |to| = 4.64244 & | t | = 3.182
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -4.6424 ) = 0.019
hence value of p0.05 > 0.019,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -4.642
critical value: -3.182 , 3.182
decision: reject Ho
p-value: 0.019
ANSWER: OPTION A:
To a 95% confidence, the sample DO differ- based on a t test for samples with different standard deviations.
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