Question

You work for a company that sells bags of sand. Each bag of sand should weigh 30 lbs when filled. You are determining if the machine is overfilling the bags, Suppose you randomly sample 7 jugs getting the weights: 29.5, 30.2, 30.8, 31.0,30.4, 30.6, 30.3 (a) What is the sample mean c? (b) What is the sample variance sº? What is s? (c) You wish to test whether the true mean is 30 lbs. Given the true mean of 30 lbs, if the chance that s/n takes its sample value or higher is less than 5%, then you conclude that it is unlikely that the true mean is 30 lbs. In this case, you will repair the machine. Will you repair the machine? X-1

Answer 1

Solutions a> Sample mean ñ = En 29.5+- +30.3 n 7 4 = 30.4 by Sample variance, - {(xi_nj2 n-1 (29.5–30.4)? + +(30-3-30.6) 7-1 s² C0.2366 S= 10.2366 = 10.4864 c) Rest hypothesis Ho i l=30 Hai m&30 Z = n-u 30.4-30 - 2:1757 slun 0.4864/7 Z=2.1757 P-value =0.0295 using Z-table, Two failed "P-value is less then o.os. Reject Ho. we have sufficient Evidence to support the claim