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masterblackbeltDear all, I have a doubt in hypothesis test topic, about the relationship between the difference of two means that we would like to identify and the statement of hypothesis.

For example: if we want to identify a difference of 2 between two means, we calculate in minitab the sample size starting from a specified standard deviation, a power (1-beta) of the test and a significance level alpha. When we collected the amount of samples based on the suggestion of minitab and we want to state the hypothesis, I’m not sure if I have to state the hypothesis in this wayH0: mean1<mean2

Ha: mean1>mean2or in this way

H0: mean1-mean2<2

Ha: mean1-mean2>2Thanks for your help

I’m not trying to be mean spirited but if you don’t know which hypothesis to use then you didn’t know what to tell Minitab with respect to calculation of sample size and power which means your output from Minitab may not have any bearing on the question you are trying to address.

The two hypothesis you have described apply to two different situations.

The first is one of a couple of different ways you could write a hypothesis where you have drawn two independent samples and are investigating the population means using the two sample t-test.The second is the hypothesis one would use with paired data and the test is that of the paired t-test. The reason you would use a paired t-test is because you do not have two independent populations. Paired t-tests are typically used in those situations where you have a single sample and you are comparing the measured sample responses before and after some kind of treatment.

Because it is the same population the before and after measures are not independent, they are repeated measures. The way you get back to the assessment of an independent measure is by taking the difference of the before and after measures on a sample-by-sample basis. The paired t-test is not run on the separate means of the population before and after measures – it is run on the distribution of the within individual sample differences. In a paired t-test H0 would be expressed as H0: mean of (before measure – after measure) = 0 and H1 would be expressed as mean of (before measure – after measure) not equal to 0.

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