Suppose that the proportion, p. of defective items in a large population of item

Question

Suppose that the proportion, p. of defective items in a large population of items is unknown, and that one wishes to test the following hypotheses: H_0: p = 0.2, H_1: p notequalto 0.2. Suppose also that a random sample of n - 20 items is drawn from the population. Let X denote the number of defective items in the sample, and consider a test procedure that rejects the null hypothesis if either X greaterthanorequalto 7 or X lessthanorequalto 1. Are the hypotheses simple or composite? Provide a brief explanation. Write down the critical region of the test. Compute the size of the test and the probability of Type I error. Calculate the value of the power function II(p) at the points p epsilon {0, 0,1,0,2,0.3,0.4,0.5,0.6,0.7,0.8,0.9.1} and sketch the power function, preferably using R. How does the power function relate to the probabilities of Type I and Type II error? Redo part (d) when the sample size increases to n = 50 mid to n = 100. Do you think the test Is any good? Suggest a way to modify the above test so that it remains meaningful at sample sizes other than 20.

Explanation / Answer

a) hypothesis are compostive because it depends on the proportions

b) critical region reject Ho is X > 7 or X < 1

c) Type I error will be 0.05

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.