Question

0. A machine produced 20 defective articles in a batch of 400.
After Overhauling it produced 10 defectives in a batch of
300. Has the machine improved? (Take a =0.01)
Given Z= 2.33 for one tailed test.​

Answer 1

Step-by-step explanation:

Given A machine produced 20 defective articles in a batch of 400.After Overhauling it produced 10 defectives in a batch of 300. Has the machine improved?

• Given n1 = 400
•           n2 = 300
• So the batch of defective articles produced by machine before overhauling = 20/400 = 0.05
• So batch of defective articles produced by machine after overhauling = 10/300 = 0.03
•                                        So we have n1P1 + n2P2 / n1 + n2
•                                                            = 400 x 0.05 + 300 x 0.03 / 400 + 300
•                                                            = 20 + 9 / 700
•                                                             = 29 / 700
•                                                              = 0.041
• So we can solve for P as
•                                          P = Q = 1 – P
•                                                     = 1 – 0.04
•                                                    = 0.96
• Now for the Right tailed test
•                                                  P1 – P2 / √PQ (1/n1 + 1/n2)
•                                                  0.05 – 0.03 / √0.041 x 0.96 (1/400 + 1/300)
•                                                                  0.02 / √0.0384 x 7 / 1200
•                                                                    0.02 / √0.000224
•                                                                      0.02 / 0.0149
•                                                                             = 1.3422
• Since Z = 1.3422, and the table value is 1.645, after overhauling, the machine has not improved.

Reference link will be

https://brainly.in/question/2364062