Question

Can you please teach me how to do this question on Minitab. Thanks

A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows:

8.24       8.25     8.20       8.23        8.24

8.21        8.26      8.26       8.20       8.25

8.23        8.23      8.19       8.28       8.24

(a) Check the assumption of normality for rod diameter.

(b) Calculate a 95% two-sided confidence interval on mean rod diameter.

(c) Calculate a 95% upper confidence bound on the mean. Compare this bound with the upper bound of the two-sided confidence interval and discuss why they are different

Answer 1

(a)

From above probability plot and AD test (since p-value>0.05) we conclude that assumption of normality for rod diameter is valid.

(b)

One-Sample T: diameter

Variable N Mean StDev SE Mean 95% CI
diameter 15 8.23400 0.02530 0.00653 (8.21999, 8.24801)

95% two-sided confidence interval on mean rod diameter is (8.21999, 8.24801).

(c)

One-Sample T: diameter

95% Upper
Variable N Mean StDev SE Mean Bound
diameter 15 8.23400 0.02530 0.00653 8.24550

95% upper confidence bound on the mean is 8.24550.

95% upper confidence bound on the mean <Upper bound of 95% two sided confidence interval on mean diameter. This is happen because we use $t_{0.025,14}=2.1448$ for computing two sided confidence interval whereas we use $t_{0.05,14}=1.7613$ for computing 95% upper confidence bound.