Question

Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The standard deviations of road octance numbers for both formulations are known to be equal but unknown. two samples of sizes n1=8 and n2=12 are tested, and the estaimes of mean road octane numbers x̄ 1= 90.50 and x̄ 2-= 91.54, respectively. The sample standard deviation for formula 1 is s1=1.30 and the sample standard deviation for formulation 2 is s2=1.24

A. Test the hypothesis whether or not formulation 1 produces the same road octance number as formulation 2. use α =0.05

B. To construct a 95% two sided confidence interval on the differences in the mean road octane number.

Please explain without using any online software.

Answer 1

a) Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom = n1+n2-2 = 18

The critical valaue of t at 5% significance level is +/-2.101

Sonce t calculated is less than t tabulated, Fail to Reject H0.

Hence , we have enough evidence to conclude that formulation 1 produces the same road octance number as formulation 2.

b) 95% CI

df = min(n1-1, n2-1) = n1-1 = 7

The critical value of t for 7 df at 5% significance level is 2.365

= ( -2.418, 0.338)