The highway department is testing two types of reflecting pa

The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 14 bridges, and the yellow paint is applied to 14 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x₁ = 9.4, with standard deviation s₁ = 1.9. For the yellow paint the mean was x₂ = 6.8, with standard deviation s₂ = 2.2. Based on these data, can we conclude that the yellow paint has less visibility after 1 year? Use a 5% level of significance.

What is the value of the sample test statistic? (Test the difference _{1 2}. Round your answer to three decimal places.)


Find (or estimate) the P-value. (Round your answer to four decimal places.)

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=9.4
Standard Deviation(s.d1)=1.9 ; Number(n1)=14
Y(Mean)=6.8
Standard Deviation(s.d2)=2.2; Number(n2)=14
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =9.4-6.8/Sqrt((3.61/14)+(4.84/14))
to =3.35
| to | =3.35
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 13 d.f is 2.16
We got |to| = 3.34664 & | t | = 2.16
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 3.3466 ) = 0.005
Hence Value of P0.05 > 0.005,Here we Reject Ho