Question

9. 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 12 bridges, and the yellow paint is applied to 10 bridges. After a period of 1 year, reflectometer readings were made on all of these bridge end pillars. (A high reading means better visibility.) For the orange paint, the mean reflectometer reading was 9.4, and for the yellow paint, the mean was 6.9. From previous studies, the standard deviation of the orange paint is ơ-21 and the standard deviation of the yellow pant is ơ-19. Based on this data, can we conclude that the yellow paint has less visibility than the orange paint after 1 year? Use a 1% level of significance.

Answer 1

Answer

it is given that mean(xbar1) = 9.4, standard deviation(sigma1) = 2.1, sample size(n1) = 12 for orange paint

and mean(xbar2) = 6.9, standard deviation(sigma2) = 1.9, sample size(n2) = 10 for yellow paint

Null hypothesis:- $H_o : \mu_1 - \mu_2 = 0$

Alternate hypothesis:- $H_a : \mu_1 - \mu_2 > 0$

test statistics z = $((\bar{x}_1-\bar{x}_2)-(\mu_1- \mu_2))/\sqrt{ ( \sigma_1^2/n_1) + (\sigma_2^2 / n_2 ) }$

$= ( ( 9.4-6.9 )-(0))/\sqrt{ ( 2.1^2/12) + (1.9^2 / 10 ) }$

= 2.5 / 0.8535

= 2.93

Using z distribution table, check 2.9 in left most column and 0.03 in top most row, select the intersecting cell, we get

p value = 0.0017

p value is less than 0.01 significance level, rejecting the null hypothesis.

We can conclude that the yellow paint has less visibility than the orange paint after 1 year