Question

Problem #1.

            The emission rates were measured from a sample of 50 engines. The observed value of the sample mean is 92 and the sample standard deviation was s = 21. It is desired to assess the plausibility that the population mean is 100 or more.

            You need to set up a hypothesis test for a level of significance of 0.05. For this purpose, you need to state the Null and Alternative hypothesis, define the rejection and non-rejection regions, and state your conclusion of the test.

Problem #2

The space collars for a transmission countershaft have a thickness specification of 38.98 -39.02 mm. The process that manufactures the collars is supposed to be calibrated so that the mean thickness is 39.00 mm. A sample of six collars is drawn and measured for thickness. The six thicknesses in mm are 39.030, 38.997, 39.012, 39.008, 39.019, and 39.002.

1. Stablish a hypothesis test for a level of significance of 0.10 to evaluate the need to recalibrate the process. State your conclusions;
2. Calculate and report the 90% confidence interval for the population mean.

Answer 1