# Difference Between Two Population Means

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 x-bar = 18.12 kgf/cm^2 for the modified mortar (m = 40) and y-bar = 16.87 kgf/cm^2 for the unmodified mortar (n = 32). Let u_1 and u_2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (see attachment)

a. Assuming the sigma_1 = 1.6 and sigma_2 = 1.4, test H0: u_1 and u_2 = 0 versus Ha: u_1 - u_2 > 0 at level 0.1.

b. Compute the probability of a type II error for the test of part (a) when u_1 - u_2 = 1.

c. Suppose the investigator decided to use a level 0.05 test and wished Beta = 0.10 when u_1 - U_2 = 1. If m = 40, what value of n is necessary?

d. How would the analysis and conclusion of part (a) change is sigma_1 and sigma_2 were unknown but s_1 = 1.6 and s_2 = 1.4?

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Math Probability and Statistics II Problem

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The attached file is the problem. The problem is Hypothesis testing with z test and confidence interval. Please be very detailed with the answer. I need detailed, clear explanation. ...

#### Solution Summary

This solution conducts a Z-test to reject or accept the null hypothesis, determines the probability of a type II, and calculates the standard deviation using a t-test.