Exercise 117 Consider the following hypotheses H0 sigma2 20

Exercise 11-7 Consider the following hypotheses: H0: sigma^2 = 200 HA: sigma^2 not equal to 200 Approximate the p-value based on the following sample information, where the sample is drawn from a normally distributed population. Use Table 3. a. s^2 = 300: n = 25 0.05

Solution

(a)

The degree of freedom =n-1=25-1=24

The test statistic is

chisquare= (n-1)*s^2/o^2

=24*300/200

=36

The p-value= P(X^2 with df=24 >36) =0.0549 (from chisquare table)

Answer: 0.05<p-value<0.1

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(b)

The test statistic is

chisquare= (n-1)*s^2/o^2

=24*100/200

=12

The p-value= P(X^2 with df=24 <12) =0.02009 (from chisquare table)

Answer: p-value <0.02

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(c)

S^2=300 , do not reject the null hypothesis

S^2=100, reject the null hypothesis.