Question

The two companies manufacture a piece of plastic used in automobile production. This plastic piece is subject to wear during use. Therefore, it is desired to compare the amount of wear of plastic parts produced by the two companies. Friction wear was applied by taking samples of 25 units randomly from both companies and after 1000 cycles wear amounts were observed. The average wear for the first company was 20 mg / 1000 cycles and the standard deviation of wear was 1.5 mg / 1000 cycles, the average for the second company was 12 mg / 1000 cycles, and the wear standard deviation was 1.8 mg / 1000 cycles. It is assumed that the wear amount of both masses shows normal distribution with the same variance.

a- Establish my 98% confidence interval for the difference between the average of wear amount of plastic parts produced by the two companies. Interpret the result. Can it be said that the amount of wear of the plastic material produced by the first company is higher?

b- Create the 95% confidence interval for the average amount of wear of the plastic part produced by the second company. Interpret the result.

Answer 1

a)

null and alternative hypothesis are

confidence interval calculations

reject null hypothesis because confidence interval not contains zero.so we can conclude that the amount of wear of the plastic material produced by the first company is higher.

b)