Question

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

Ans 1 ) the null and alternative hypothesis is

Ho: μ = 39

Ha: μ ≠ 39 (two tailed )

using minitab>stat>basic stat>one sample T

we have

One-Sample T: data

Test of μ = 39 vs ≠ 39

Variable N Mean StDev SE Mean 90% CI T P
data 6 39.0113 0.0119 0.0049 (39.0015, 39.0211) 2.33 0.067

the p-value of test statistic is 0.067 since the p-value is less than 0.10 so we reject Ho and conclude that  the mean thickness is not 39.00 mm.

Ans 2 ) the 90% confidence interval is (39.0015, 39.0211)

we are  90% confident that the  population mean thickness lies in between 39.0015, 39.0211