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Chapter 9: Q2E (page 604)
2. Suppose that a random variable X has the F distribution with three and eight degrees of freedom. Determine the value of c such that Pr(X>c) = 0.975
The required value of c is 0069.
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1. Consider again the situation described in Exercise 11 of Sec. 9.6. Test the null hypothesis that the variance of the fusion time for subjects who saw a picture of the object is no smaller than the variance for subjects who did see a picture. The alternative hypothesis is that the variance for subjects who saw a picture is smaller than the variance for subjects who did not see a picture. Use a level of significance of 0.05.
Suppose that the proportion p of defective items in a large, manufactured lot is unknown, and it is desired to test the following simple hypotheses:
H0: p = 0.3,
H1: p = 0.4.
Suppose that the prior probability that p=0.3 is 1/4, and the prior probability that p = 0.4 is 3/4; also suppose that the loss from choosing an incorrect decision is 1 unit, and the loss from choosing a correct decision is 0. Suppose that a random sample of n items is selected from the lot. Show that the Bayes test procedure is to reject H0 if and only if the proportion of defective items in the sample is greater than
\begin{aligned}log\frac{7}{6}+\frac{1}{n}log\frac{1}{3}-log\frac{9}{14}\end{aligned}
Suppose that \({X_1},....,{X_{10}}\)form a random sample from a normal distribution for which both the mean and the variance are unknown. Construct a statistic that does not depend on any unknown parameters and has the \(F\)distribution with three and five degrees of freedom.
Suppose that X1,鈥�.., Xn forms a random sample from the normal distribution with unknown mean 碌 and unknown variance 蟽2. Classify each of the following hypotheses as either simple or composite:
a) H0 : 碌 = 0 and 蟽=1
b) H0 : 碌 > 3 and 蟽<1
c) H0 : 碌 = -2 and 蟽2<5
d) H0 : 碌 = 0
Suppose that a random sample of eight observationsX1,鈥�.,Xs is taken from the normal distribution with the unknown mean 碌 and unknown variance 蟽2, and it is desired to test the following hypotheses:
H0 : 碌 = 0
H1 : 碌鈮� 0
Suppose also that sample data are such that \begin{aligned}\sum_{i-1}^{8}X_{i}=-11.2\end{aligned} and \begin{aligned}\sum_{i-1}^{8}X_{i}^{2}=43.7\end{aligned}
if a symmetric t- test is performed at the level of significance 0.10 so that each tail of the critical region has probability 0.05, should the hypothesis H0be rejected or not?
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