Suppose again, as in Exercise 9, that a random sampleof 10 observations is taken from the normal distributionwith unknown mean µ and unknown variance o?, but suppose now that the following hypotheses are to be tested atthe level of significance 0.05: Ho σ?=4, Hi:0²# 4. Suppose that the null hypothesis Ho is to be rejected ifeither S2sq or s2 z c2, where the constants c, and cz areto be chosen so that, when the hypothesis H, is true, Pr(S, c2) = 0.025. Determine the values of c, and c2.

Suppose again, as in Exercise 9, that a random sampleof 10 observations is taken from the normal distributionwith unknown mean µ and unknown variance o?, but suppose now that the following hypotheses are to be tested atthe level of significance 0.05: Ho σ?=4, Hi:0²# 4. Suppose that the null hypothesis Ho is to be rejected ifeither S2sq or s2 z c2, where the constants c, and cz areto be chosen so that, when the hypothesis H, is true, Pr(S, c2) = 0.025. Determine the values of c, and c2.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose again, as in Exercise 9, that a random sampleof 10 observations is taken from the
normal distributionwith unknown mean p and unknown variance o?, but suppose now that the
following hypotheses are to be tested atthe level of significance 0.05:
Hoio² = 4,
H1:0²# 4.
Suppose that the null hypothesis Ho is to be rejected ifeither s2sc or s2 2 cz, where the
constants c, and cz areto be chosen so that, when the hypothesis H, is true,
Pr(S, <c1) = Pr(S > c2) = 0.025.
Determine the values of c, and c2.
9. Suppose that a random sample of 10 observations
X1, ..., X10 is taken from the normal distribution with
unknown mean µ and unknown variance o², and it is de-
sired to test the following hypotheses:
Но: о? <4,
H: о2> 4.
Suppose that a test of the form described in Exercise 8 is
to be carried out at the level of significance ao = 0.05. If
the observed value of S? is 60, should the hypothesis Ho
be rejected or not?

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