1) For comparing means of two populations, for a given alpha error, what can you

Question

1) For comparing means of two populations, for a given alpha error, what can you do to increase power of test?

2) Consider two separate mean comparisons: (1) H0: µ1= µ2 and (2) H0: µ3=µ4, with KNOWN variances:

If 1 and 2 are both higher than 3 and 4, which hypothesis test (1 or 2) will need higher sample size for a given alpha error?

For a given sample size, If 1 and 2 are both higher than 3 and 4, and if (µ1-µ2) is equal to (µ3-µ4), which hypothesis test (1 or 2) will have more power of test?

3) What is the main advantage of pair-wise comparison of two means?

Explanation / Answer

Dear student please post the question one at a time,

1)The power of a hypothesis test is affected by two factors.

a)Sample size (n). Other things being equal, the greater the sample size, the greater the power of the test.

b)The "true" value of the parameter being tested. The greater the difference between the "true" value of a parameter and the value specified in the null hypothesis, the greater the power of the test. That is, the greater the effect size, the greater the power of the test.

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