# Question: A random sample of size 64 is to be used

A random sample of size 64 is to be used to test the null hypothesis that for a certain age group the mean score on an achievement test (the mean of a normal population with σ2 = 256) is less than or equal to 40.0 against the alternative that it is greater than 40.0. If the null hypothesis is to be rejected if and only if the mean of the random sample exceeds 43.5, find

(a) The probabilities of type I errors when µ = 37.0, 38.0, 39.0, and 40.0;

(b) The probabilities of type II errors when µ = 41.0, 42.0, 43.0, 44.0, 45.0, 46.0, 47.0, and 48.0. Also plot the power function of this test criterion.

(a) The probabilities of type I errors when µ = 37.0, 38.0, 39.0, and 40.0;

(b) The probabilities of type II errors when µ = 41.0, 42.0, 43.0, 44.0, 45.0, 46.0, 47.0, and 48.0. Also plot the power function of this test criterion.

## Answer to relevant Questions

The sum of the values obtained in a random sample of size n = 5 is to be used to test the null hypothesis that on the average there are more than two accidents per week at a certain intersection (that λ > 2 for this Poisson ...A single observation of a random variable having an exponential distribution is used to test the null hypothesis that the mean of the distribution is θ = 2 against the alternative that it is θ = 5. If the null hypothesis ...Given large random samples from two binomial populations, show that the null hypothesis θ1 = θ2 can be tested on the basis of the statistic Where In the test of a certain hypothesis, the P-value corresponding to the test statistic is 0.0316. Can the null hypothesis be rejected at the (a) 0.01 level of significance; (b) 0.05 level of significance; (c) 0.10 level of ...Five measurements of the tar content of a certain kind of cigarette yielded 14.5, 14.2, 14.4, 14.3, and 14.6 mg/cigarette. Assuming that the data are a random sample from a normal population, use the four steps on page 354 ...Post your question