Question

Certain pesticide packed into bags by machine. A random sample of 10 bags is drawn and their contents are found to be as follows
content: 50,49,52,44,45,48,46,45,49,45
test if average can be taken as 50kg

Answer 1

Step-by-step explanation:

Given Certain pesticide packed into bags by machine. A random sample of 10 bags is drawn and their contents are found to be as follows  content: 50,49,52,44,45,48,46,45,49,45  test if average can be taken as 50 kg

Null hypothesis :  

Ho = μ = 50 kg, so average packing is 50 kg

Another hypothesis h1 : μ =/ 50 kg

50 49 52 44 48 46 45 49 45

We know that Mean = 473 / 10, So x bar = 47.3

x               x(x – x bar)            x^2  

50                   2.7                    7.29

49                   1.7                    2.89

52                   4.7                   22.09

44                  -3.3                   10.89

45                  -2.3                     5.29

48                   0.7                      0.49

46                   - 1.3                     1.69

45                   - 2.3                     5.29

49                      1.7                     2.89

45                     - 2.3                    5.29

473                                           64.1

We know that variance = ∑ x^2 / n

                                        = 64.1 / 10

                        So S^2 = 6.41

Test statistic t = x bar – μ / √s^2 / n – 1

                      = 47.3 – 50 / √6.41 / 9

                      = - 2.7 / √0.712

                       = - 2.7 / 0.843

                       = - 3.2

Therefore h 1 is greater than t, and ho is rejected.