32. The diameter of a ball bearing was measured by 10 ectors, each using two dif

Question

32. The diameter of a ball bearing was measured by 10 ectors, each using two different kinds of calipers. The insp results were Inspector Caliper 1 0.265 0.265 0.266 0.267 0.267 0.265 0.267 0.267 0.265 0.268 Caliper 2 0.264 0.265 0.264 0.266 0.267 0.268 0.264 0.265 0.265 0.267 2 4 10 (a) Is there a significant difference between the means of the population of measurements from which the two samples were selected? Use = 0.05. b) Find the P-value for the test in part (a). e) Construct a 95 percent confidence interval on the dif- terence in mean diameter measurements for the two types of calipers.

Explanation / Answer

lets analyse this using the open source statistical package R

The complete R snippet is

caliper1 <- c(.265,.265,.266,.267,.267,.265,.267,.267,.265,.268)
caliper2 <- c(.264,.265,.264,.266,.267,.268,.264,.265,.265,.267)

# perform the test
t.test(caliper1,caliper2)

The results are

> t.test(caliper1,caliper2)

   Welch Two Sample t-test

data: caliper1 and caliper2
t = 1.2104, df = 17.101, p-value = 0.2426 ## as the p value is less than 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.0005195805 0.0019195805
sample estimates:
mean of x mean of y
0.2662 0.2655

Hypothesis

H0: There is no difference in the mean values of the caliper measurements

H1 : H0: There is a statistical difference in the mean values of the caliper measurements

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