im having trouble wit this problem **Hypothesis Test for the Difference Between Two Population Means**An electrician aims to determine if batteries manufactured by two different companies have significantly different voltages. The voltage of 128 batteries from each manufacturer was measured, and the population standard deviations are known. The results are provided in the table below:| Manufacturer | Sample Mean Voltage (millivolts) | Population Standard Deviation ||--------------|----------------------------------|-------------------------------|| A | 112 | 5 || B | 111 | 3 |**Tasks:**1. **Select the Type of Hypothesis Test:** Determine what type of hypothesis test should be performed.2. **Calculate the Test Statistic:** Identify the test statistic for this comparison.3. **Assess Evidence at Significance Level:** Decide whether there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different at the α = 0.1 significance level.This exercise helps students understand the application of hypothesis testing in evaluating differences between two population means, particularly when the population standard deviations are known.

Solution: Given information: n1= 128 Sample size of manufacture A n2=128 Sample size of manufacture Bx1= 112 Sample mean of manufacture A x2= 111 Sample mean of manufacture Bσ1= 5 Population standard deviation of manufacture A σ2= 3 Population standard deviation of manufacture B α=0.10 Level of significance We should used two sample z test because population standard deviation is known. Type of test : z test. To test the hypothesis Ho:μ1=μ2 VS Ha:μ1≠μ2 Test statistic z = x1-x2σ12n1+σ22n2z = 112-11152128+32128z =112-11125128+9128z =112-1110.1953125+0.0703125z=112-1110.265625z=10.515388= 1.940286z= 1.94 Test statistic z = 1.94 To find p value p value = 2*P( Z> 1.94) p value = 2* 0.0262 From Z table p value = 0.0524 Decision: p value < α=0.10 Reject the null hypothesis Conclusion: There is sufficient evidence to support the claim that the voltage of the batteries by two manufactures is different at the α=0.10 significance level. Yes