Question

1. A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters. Compute the p-value for testing whether the population mean is larger than 6 centimeters.

NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.

2. A sample of 81 observations has been selected to test whether the population mean is smaller than 15. The sample showed an average of 14.3 and a standard deviation of 2.7. You want to test this hypothesis at 93% level of confidence using the critical value approach. First, compute the critical value and the test statistics associated with this test. Second, compute the difference between the test statistic and the critical value (test statistic - critical value). What is this

NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN. MAKE SURE YOU INDICATE THE SIGN OF THIS DIFFERENCE CORRECTLY.

Answer 1

1)MINITAB OUTPUT:

  One-Sample T

Test of mu = 6 vs > 6

95%
Lower
N Mean StDev SE Mean Bound T P
121 6.08000 0.44000 0.04000 6.01369 2.00   0.02387926

  p-value=0.0239 here.p-value<0.05 hence at 5% significance level we can conclude that the mean is larger than 6cm.

2)One sample T

Test of mu=15 vs <15

alpha=0.07

critical value=

value of test statistic=

difference between test statistic and critical value=-0.8427

Since, test statistic<critical value we reject the null and conclue that the mean is smaller than 15.