For a consumer of aspirin, it is important that the product be consistent with r
ID: 3358124 • Letter: F
Question
For a consumer of aspirin, it is important that the product be consistent with respect to amount of active aspirin in a tablet. Here are the amounts of aspirin contained in samples drawn from the production of two different manufacturers (M1 and M2). Do the data indicate any differences with respect to consistency in amount? Be sure to include a statement to be tested, describe the random variables involved and assumptions about them, level of significance, statistical hypotheses, test statistic, and the critical region. Use SPSS to do it, include the SPSS output in your response and explain how you used it to answer the question.
M1 M2
353.85 355.55
354.86 356.87
354.71 388.61
353.65 370.44
343.64 363.27
354.29 356.15
359.91 352.46
354.29 357.72
355.05 308.22
345.82 351.06
M1 M2
353.85 355.55
354.86 356.87
354.71 388.61
353.65 370.44
343.64 363.27
354.29 356.15
359.91 352.46
354.29 357.72
355.05 308.22
345.82 351.06
Explanation / Answer
Given that,
mean(x)=353.006
standard deviation , s.d1=4.7368
number(n1)=10
y(mean)=356.035
standard deviation, s.d2 =20.1345
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =353.006-356.035/sqrt((22.43727/10)+(405.39809/10))
to =-0.4631
| to | =0.4631
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 2.262
we got |to| = 0.46309 & | t | = 2.262
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.4631 ) = 0.654
hence value of p0.05 < 0.654,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -0.4631
critical value: -2.262 , 2.262
decision: do not reject Ho
p-value: 0.654
we do not have enough evidence to support the claim
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