Perform the hypothesis testing for the following problems.(Please show complete steps/solutions)

In order to determine the effect of music on productivity in a toy firm, the manager divided the 16 workers into 2 groups. Eight were put in one section of the shop and were allowed to listen to taped music while working, while the other eight were put in another section, without music. The total output for each group was recorded daily for one week, after which the averages and standard deviations were computed. The 8 workers who listened to music had an average of 320 units with a standard deviation of 10 units. The other 8 had an average of 312 units with a standard deviation of 16 units. Can the manager conclude that music increases the productivity of workers at = 0.01 ?

IS MY SOLUTION CORRECT?

REV PAPAYA 1= 16 asynchronous # 3 No. w / DATE w/of 3 n1 8 n2 : 8 X 1 : 320 units xy = 312 units S, = 10 units Sz = 16 units df = n, + 12 - 2 = 8 + 8 -2 C = 0.01 = 16 - 2 = 14 music increases > Ho : W, = W 2 Ha : wis MZ ( one - tailed test ; right side ) 2. 6 24 Alpha : 2. 624 4 df= 14, f= 0.01 (+-table) to " X 1 - X 2 ( n , - 1 ) s , 2 + ( n 2 - 1 ) s ( 1 + !) n, + n 2 4 - 2 320 - 312 (8- 1) ( 102 ) + (8-1) ( 142) 8 + 8 - 2 8 g = 0.1797 CATTLEYA NOTE Decision: Accept Ho (7 ) ( 100 ) + ( 7 ) ( 256 ) (0. 25) Conclusion : Music doesn't increase 14 productivity