Question

3. Two agencies supply temporary workers for light manufacturing. Both agencies give their workers a test of dexterity. The two populations at a particular time have the following means and standard deviations: Agency K Agency R Mean 78.28, 75.79 Standard deviation 9.63, 11.25 Samples of 28 workers from agency K and 32 from agency R are sent to a manufacturer on one particular day. Is there significant difference between these 2 groups/agencies? Use a 1 % significance level and a two-sided test. Interpret obtained result in terms of given example.

Answer 1

x1 = 78.28, x2 = 75.79, s1 = 9.63, s2 = 11.25, n1 = 28, n2 = 32

H0: μ1 = μ2

H1: μ1 ≠ μ2

Test statistic =

[(x1 - x2)-(µ1-µ2)] / [((s12(n1-1) + s22(n2-1))/(n1+n2-2))^0.5*(1/n1+1/n2)^0.5]

= ((78.28-75.79)-0)/((((9.63*9.63*27)+(11.25*11.25*31))/(28+32-2))^0.5*(1/28+1/32)^0.5)

=0.914

Degrees of freedom = n1+n2-2 = 28+32-2 = 58

Level of significance = 0.01

Critical value (Using Excel function T.INV.2T(probability,df)) = T.INV.2T(0.01,58) = 2.663

Since test statistic is less than critical value, we do not reject the nullhypothesis and conclude that μ1 = μ2.

There is no significant difference between these 2 groups/agencies.