# Question: Suppose we are testing the hypotheses H0 1 2 H1

Suppose we are testing the hypotheses

H0 : 1 2

H1 : 1 2

where 12 and 22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?

H0 : 1 2

H1 : 1 2

where 12 and 22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?

**View Solution:**## Answer to relevant Questions

There is a typographical error in the hypotheses (should be 22) in early printings of the 7th edition; this solution is for the correct hypotheses. Develop a test for the hypotheses H0 : 1 22 H1 : 1 ...Compare the mean etch uniformity values at each of the C2F6 flow rates from Exercise 4.33 with a scaled t distribution. Does this analysis indicate that there are differences in mean etch uniformity at the different flow ...A plant distills liquid air to produce oxygen, nitrogen, and argon. The percentage of impurity in the oxygen is thought to be linearly related to the amount of impurities in the air as measured by the “pollution count” ...Reconsider the patient satisfaction data in Table 4E.11. Fit a multiple regression model using both patient age and severity as the regressors. (a) Test for significance of regression. (b) Test for the individual ...Suppose that you are testing the following hypotheses where the variance is unknown: H0 : 100 H1 : 100 The sample size is n = 25. Find bounds on the P-value for the following values of the test statistic. (a) ...Post your question