An experiment was conducted to estimate the strength of certain kind of braided cord after weathering. The strengths of 56 pieces of cord that had been weathered for 30 days were investigated. The 56 pieces of cord were placed simultaneously in the tensile strength device. The device applies an rising amount of force till the cord fails.
These are the cord strengths:
19.7 21.6 21.9 23.5 24.2 24.4 24.9 25.1
26.4 26.9 27.6 27.7 27.9 28.4 29.8 30.7
31.1 31.1 31.7 31.8 32.6 34.0 34.8 34.9
35.1 36.6 37.0 37.7 38.7 38.7 39.0 39.6
40.0 41.4 41.4 41.8 42.2 43.5 44.5 45.0
45.5 45.9 46.3 46.7 46.7 47.0 47.0 47.4
47.6 48.6 48.8 57.9 58.3 67.9 84.2 97.3
The manufacturer of the cord is planning some major changes to their cord which will raise the tensile strength. After making the changes in the product, it will be necessary to run the large study to validate that the changes have in fact raised the tensile strength. Find out the minimum sample size vital to be at least 95% confident that the tensile strengths obtained in sample will cover 90% of tensile strengths produced in new manufacturing process.