Let Y be b(100, p). To test Ho: p = 0.08 against H1: p < 0.08, we rejectHo and acceptH1 if and only if VS 6.

(a) Determine the significance level a of the test.

(b) Find the probability of the Type II error if, in fact, p = 0.04.

QUESTION38

A bowl contains two red balls, two white balls, and a fifth ball that is either red or white. Let p denote the probability of drawing a red ball from the bowl. We shall test the simple null hypothesis Ho: p = 3/5 against the simple alternative hypothesis H1: p = 2/5. Draw four balls at random from the bowl, one at a time and with replacement. Let X equal the number of red balls drawn.

(a) Define a critical region C for this test in terms of X.

(b) For the critical region C defined in part (a), find the values of a and 13.

QUESTION39

Let Y be b(192, p). We reject Ho: p = 0.75 and acceptH1: p > 0.75 if and only if Y? 152. Use the normal approximation to determine (a) a= P(11 ? 152; p= 0.75). (b) p = P(Y < 152) when p= 0.80.

QUESTION40

If a newborn baby has a birth weight that is less than 2500 grams (5.5 pounds), we say that the baby has a low birth weight. The proportion of babies with a low birth weight is an indicator of lack of nutrition for the mothers. For the United States, approximately 7% of babies have a low birth weight. Let p equal the proportion of babies born in the Sudan who weigh less than 2500 grams. We shall test the null hypothesis Ho: p = 0.07 against the alternative hypothesis H1: p > 0.07. In a random sample of n = 209 babies, y = 23 weighed less than 2500 grams.

(a) What is your conclusion at a significance level of a = 0.05? (b) What is your conclusion at a significance level of a = 0.01? (c) Find the p-value for this test.