Question

5. 130 pointsl The diameter of a ball bearing was measured by 12 inspectors each using two different kinds of calipers. The results are as follows: nspector 0.264 0.265 0.266 0.264 0.266 0.267 0.265 0.267 0.2 0.265 0.265 10 0.269 69 Is there a significant difference between the means of the population of measurements from which the two samples were selected? Use α Find the p-value for the test in part (a) Construct a 95% confidence interval on the difference in mean diameter measurements for It is important to detect a deviation of 0.001 between the calipers with a probability of 90%. Will we able to accomplish this? If not, what sample size will be needed to obtain a 90% detection probability? Use signed test to determine the significance. Do this by hand as well as by using MATLAB a. 0.05. b. c. the two types of pers. d. e.

Answer 1

As HOMEWORKLIB RULES protocol , i shall answer atleast four subparts of this question

a and b).This is a simple problem related to testing the level of siginificance in difference in reading between two population samples.

The dataset is drawn from two independent populations as given below.

We shall conduct the t test for two independent samples and try to encompass all the questions asked .

	Inspector	Caliper 1	Caliper2
	1	0.265	0.264
	2	0.265	0.265
	3	0.266	0.264
	4	0.267	0.266
	5	0.267	0.267
	6	0.265	0.268
	7	0.267	0.264
	8	0.267	0.265
	9	0.265	0.267
	10	0.268	0.268
	11	0.268	0.269
	12	0.265	0.269
	Mean	0.266	0.266
Std deviation		0.001	0.002
	n	12	12

Hence we cant conclude with significance that caliper 1 measurement is any different from that of caliper 2.

c). Now that we have conducted the hypothesis testing ,lets now focus on finding the confidence interval of the difference of the means of samples given above.

d). Sample size calculator

Now we need to check if the zone of limits that we have created (-0.001, 0.001) is good enough to measure a value of 0.001 with a probability of 90 % or not.

We are given with all data and lets try to find the sample size required independently.

Thus minimum sample size required is 11 and we have samples of size 12. Thus it substanctiates the fact that from the confidence interval found above, we can capture diffrence in caliper reading of 0.001 with atleast 90 % probability.