Design of experiments-hypothesis test or regression analysis?

Question

Perform the appropriate hypothesis test or regression analysis as required. 

Data from two cookie making processes were collected. The value's units are grams. The purpose was to determine if the two processes are producing cookies of the same weight. Past cookie data make it plausible to consider cookie weight is normally distributed. Perform the appropriate test to answer the question, "Is there a difference at 95% confidence?"

Machine A Data: 11.5 11.7 11.8 11.7 11.9 11.8 11.3 11.8 11.4 11.7

Machine B Data: 11.7 11.5 11.9 11.6 12.0 12.1 12.0 12.0 11.9 11.9

Merlyn · Accepted Answer

Use a two sample t test for the difference in means for small samples.  This is a valid test because you are told that the data comes from a normal population.  if it did not then you could not use this testing method.

if you have R then here is the code to do this test.  if not, then you can get it for free from www.r-project.org

machA <- c(11.5, 11.7, 11.8, 11.7, 11.9, 11.8, 11.3, 11.8, 11.4, 11.7)
machB <- c(11.7, 11.5, 11.9, 11.6, 12.0, 12.1, 12.0, 12.0, 11.9, 11.9)
t.test(machA,machB)

the results of the test are:

        Welch Two Sample t-test

data:  machA and machB 
t = -2.2875, df = 18, p-value = 0.03449
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.38368889 -0.01631111 
sample estimates:
mean of x mean of y 
    11.66     11.86 

the p-value is lower than 5% and therefore we can reject the null hypothesis that the means are equal and conclude that the alternate hypothesis is true, the means are different.

Anonymous · Answer

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Design of experiments-hypothesis test or regression analysis?

2 Answers