Answer:
The materials price variance is usually the responsibility of the purchasing manager. The materials quantity and labor efficiency variances are usually the responsibility of production managers and supervisors.
155 is your answer lmk if you need anything else
Answer:
a
The estimate is ![- 0.0265\le K \le 0.0465](https://tex.z-dn.net/?f=-%200.0265%5Cle%20%20K%20%5Cle%20%200.0465)
b
Method B this is because the faulty breaks are less
Step-by-step explanation:
The number of microchips broken in method A is ![n_1 = 400](https://tex.z-dn.net/?f=n_1%20%3D%20400)
The number of faulty breaks of method A is ![X_1 = 32](https://tex.z-dn.net/?f=X_1%20%3D%2032)
The number of microchips broken in method B is ![n_2 = 400](https://tex.z-dn.net/?f=n_2%20%20%3D%20400)
The number of faulty breaks of method A is ![X_2 = 32](https://tex.z-dn.net/?f=X_2%20%3D%2032)
The proportion of the faulty breaks to the total breaks in method A is
![p_1 = \frac{32}{400}](https://tex.z-dn.net/?f=p_1%20%3D%20%5Cfrac%7B32%7D%7B400%7D)
![p_1 = 0.08](https://tex.z-dn.net/?f=p_1%20%3D%200.08)
The proportion of the faulty to the total breaks in method B is
![p_2 = 0.07](https://tex.z-dn.net/?f=p_2%20%3D%20%200.07)
For this estimation the standard error is
![SE = \sqrt{ \frac{p_1 (1 - p_1)}{n_1} + \frac{p_2 (1- p_2 )}{n_2} } }](https://tex.z-dn.net/?f=SE%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7Bp_1%20%281%20-%20p_1%29%7D%7Bn_1%7D%20%20%2B%20%5Cfrac%7Bp_2%20%281-%20p_2%20%29%7D%7Bn_2%7D%20%7D%20%7D)
substituting values
![SE = \sqrt{ \frac{0.08 (1 - 0.08)}{400} + \frac{0.07 (1- 0.07 )}{400} } }](https://tex.z-dn.net/?f=SE%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B0.08%20%281%20-%200.08%29%7D%7B400%7D%20%20%2B%20%5Cfrac%7B0.07%20%281-%200.07%20%29%7D%7B400%7D%20%7D%20%7D)
![SE = 0.0186](https://tex.z-dn.net/?f=SE%20%3D%200.0186)
The z-values of confidence coefficient of 0.95 from the z-table is
![z_{0.95} = 1.96](https://tex.z-dn.net/?f=z_%7B0.95%7D%20%3D%20%201.96)
The difference between proportions of improperly broken microchips for the two breaking methods is mathematically represented as
![K = [p_1 - p_2 ] \pm z_{0.95} * SE](https://tex.z-dn.net/?f=K%20%3D%20%5Bp_1%20-%20p_2%20%5D%20%5Cpm%20z_%7B0.95%7D%20%2A%20SE)
substituting values
![K = [0.08 - 0.07 ] \pm 1.96 *0.0186](https://tex.z-dn.net/?f=K%20%3D%20%5B0.08%20-%200.07%20%5D%20%5Cpm%201.96%20%2A0.0186)
![K = - 0.0265 \ or \ K = 0.0465](https://tex.z-dn.net/?f=K%20%20%3D%20%20-%200.0265%20%5C%20or%20%20%5C%20K%20%20%3D%20%200.0465)
The interval of the difference between proportions of improperly broken microchips for the two breaking methods is
![- 0.0265\le K \le 0.0465](https://tex.z-dn.net/?f=-%200.0265%5Cle%20%20K%20%5Cle%20%200.0465)