Question

The aptitude test scores of the types of technical operators are analyzed. Two random samples were taken with the following results:

Operator's antiquity	n	mean	standard deviation
5 or more years	12	123 pts	29 pts
less than 5 years	16	116 pts	35 pts

a) Determine if there is evidence evidence that the average points in the test is higher for the technical operators with greater seniority. Use a level of significance of 0.1

b) Determine if there is evidence that the standard deviation of the score in the test is equal or not for all types of operators, use a level of significance of 0.1.

Answer 1

"Let 1: 5 or more years 2: less than 5 years n_1 = 12 n_2 = 16 x^bar_1 = 123 x^bar_2 = 116 s_1 = 29 s_2 = 26 a) n_0: u_1 = u_2 v/s n_a: u_1 > u_2 under no test statistics is t = x^bar_1 - x^bar_2/squareroot s^2_1/n_1 + s^2_1/n_2 = 123 - 116/squareroot 29 times 29/12 + 35 times 35/16 = 7/12.1097 = 0.5780 alpha = 0.1 t_x_12, upsilon upsilon = min (n - 1, n - 2) = 11 t _0.05, 11 = 1.796