Question

1. An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in =18.12 kgf/cm2 for the modified mortar (m=40) and j = 16.87 kgf/cm2 for the unmodified mortar (n=32). Let Hy and My be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. a. Assuming that ay =1.6 and az =1.4, test Ho:41-42 S Oversus H2:47-12 > 0 at level 1%. b. Compute the probability of a type II error for the test of part (a) when H1-H2 =1.

Answer 1

Date Page solution's at given that u, denotes the true age tension bond strengthy to modified motory and My denotes the true age tension bond strengths to unmodified mostars. The null and alternative hypothesis are stated as follows: Hill, - M2=o. versus. : مولر - رلر !هل The population standard deviations for the both groups are given of O = 1.6 ando... The sample information to the given scenario Es summarized as below: sample Motor Hodified x = 18-12ugflem? 116. 87 kgf/cm? sample size mean. me40 un mo. defied ns32

Page (a) Define the statistics, under the null hypo- they ay below! Ž= (-9) (-9) -AO 18-12-16.87 +1:42 40 32 1.25 0.354 53.53 Fox=0.0f the critical value 9 Z0.01=2.33. Here, observe that Zeal (3.53) > Z2 62.33), so Reject the null hypothesis. there is sufficient evidence to conclude that the true age tension bond strengthe do modified motory s greater than age tension bond strengthy for unmodified molass

Page (b) the true difference between the meary of the two groups is given af olar. By definition, the probability of type IP Zoa-do osega from partca), 70.01 - 2.33 and ore-y=0.354 substitute the known values; BC1= ¢ (Zie d'Ao eroor is; B(1)=0 a'-se] ose- = 2.33 - ole 0-354 (-0.50). 50.3088) Therefore, the probability of type I embly 0.3088 please Like It helps a lot for me