The structure of the development of the exercises is as follows: - Necessary calculations. - Hypothesis. - Test statistic. - Critical value or values. - Rejection region. - Conclusion.

1) An experiment was carried out to compare the resistance of two materials, obtaining the following results:

material	n	average	Standard deviacin
1	14	88	6
2	12	82	4

Assume that they are independent random samples and that they come from normal populations with unknown but equal variances. Prove to 5% significance that the strength of material 1 exceeds the strength of material 2 by more than three units.

2) Samples of 1,545 men and 1,691 women were used to compare the amount of housework performed by women and men in marriages with double economic contribution. The study indicated that 67.5% of men felt that the division of domestic tasks was fair, while 60.8% of women also perceived it as fair. Is the proportion of men who felt that the division of housework was fair higher than the corresponding proportion of women? Support your conclusion with a statistical test at the 5% level of significance. Note: Use three decimal places with the last approximated for the p-values.

3) A software engineer from a financial institution develops an algorithm that would help improve the performance of branch executives. To verify this, the average attention time of 12 executives is measured, before and after implementing the algorithm, finding the following results:

Attention times (min.)
executive	before	after
1	12	11
2	15	13
3	21	19
4	14	11
5	18	16
6	17	15
7	15	13
8	13	13
9	12	11
10	15	14
11	19	19
12	17	15

Considering that the attention times are approximately normally distributed, test with 1% significance if the algorithm managed to improve the average attention times.

A need the answers step by step. please the corrects anwers

For example, according my development, please , you comparative your answer

\fLUN MAR ME JUEVESAB JOOM FECHA Ejercicio 3 . Ejecutivo. Antes|Despues DiFerenciA. M = 12 . 12 41 J = - 1417 15 13 - 2 Sd = 0190 21 19 - 2 ho = 0jot 41 - 3 W- 1 = 11 Grades libertad 18 - 2 HI = ud - Ha yo J O OO D G VI S W N A 17 15 - 2 Ho = Md - Heso 15 13 - 2 tertico = tool; 11 13 13 O ( critico = = 2,72/ 12 11 - 1 15 14 11 19 19 12 17 16 - 1. (Despues - Antes ) (3) GotAdiet co de Prueba 6 = - 1417 -0 : - 5145 17/09/2022 12:50FECHA Ejercicio 2. / OFerencia de proporciones Datos Hombres Mujeres h = 1545 h = 1691 . - 196 1 96 3,94 Conclusion : a 5 % $ 0105. 2 /2 - 01025 @ Hi potesis differencia do proforciones. Ho PI- P2 = 0 P1 = P2 H1: P1 - P2 + 0 91 + pz . () Est: mydores puntuAles. 2 1 = 67,5 : 100 - 0, 675 P2 = 60,8 : 100 + 0,608 8 1 = 1 - 0, 675 - 0,325 82 = 1 - 0,608 + 0,392 (3) Estadistico de prueba. 01 675 - 0.608 10, 067 - 3, 94 01675 01325 + 0, 608- 10,392 10 , 0171 15 45 169 1 ( 4) 2 CRitiCO. (2 2 2 2/2 0 2 4 + 2 042) Z d. = 20.025 + 1,96 2 17/09/2022 12:50