Two different formulations of an oxygenated motor fuel are being tested to study

Question

Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The manufacturer claims that formulation 2 produces a higher road octane number than formulation 1. The variance of road octane number for formulation 1 is sigma_1^2 = 5.4, and for formulation 2 it is sigma_2^2 = 6.5. Two random samples of size n_1 = 15 and n_2 = 20 are tested, and the mean road octane numbers observed are x_1^bar = 89.6 and x_2^bar = 92.5. Assume normality. Is there evidence to support the manufacturer's claim?

Explanation / Answer

her we use t-test and

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

with null hypotheis H0:mu1=m2 and alternate hypothesis H1:mu1<mu2

t=(89.6-92.5)/(2.46*sqrt(1/5+1/20))=-2.36 with 33 df

one tailed critical t(0.05,33)=1.69 is less than the absolute value of calcuted t=2.36, so we fail to accept null hypothesis H0 and conclude that the manufacture claim is true.

follwoing calculation has been done for the above question

mean s2 n (n-1)s2 first 89.6 5.4 15 75.6 second 92.5 6.5 20 123.5 total= 182.1 11.9 35 199.1 sp2= 6.033333 sp= 2.456284

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.