Tindendo is a famous video game console manufacturer based in Kagoshima, Japan. Tindendo uses a very specific chip for its consoles currently in the market. However, Tindendo plans to research other possible suppliers that could provide these chips at least in the same quality as that ensured by the incumbent supplier.
To that end, Tindendo has found an alternative supplier. Tindendo randomly sampled 50 parts from both the incumbent and the alternative supplier and came up with a methodology and proprietary technology that could measure by how much each part deviates from the required specification.
Although switching costs are high for this particular part, Tindendo determined that they could work with the alternative supplier if the average deviation from the standard required measures for the incumbent supplier were to be 5 nanometers or higher than that for the alternative supplier.
The average variation for the samples supplied by the incumbent supplier is 54 nanometers with a standard deviation of 9 nanometers. The average variation for the samples supplied by the alternative supplier is 48 nanometers with a standard deviation of 7 nanometers.
a) Should Tindendo change its supplier if it were to use a level of significance of 5%?
b) Assume that Tindendo determined that it could work with the alternative supplier if the average deviation from the standard required measures for the incumbent supplier were to be 2 nanometers or higher than that for the alternative supplier. Should Tindendo change its supplier if it were to use a level of significance of 5%?
c) Assume that Tindendo decided to change suppliers provided that the average variation amount for the incumbent supplier is higher than that for the alternative supplier by any amount. Without calculating anything algebraically, could you determine what Tindendo should do in that case (all other inputs values stay the same)?