Question

Fill in the blank. A critical? value, z Subscript alpha z??, denotes the? _______. A critical? value, z Subscript alpha z??, denotes the ?

Answer 1

A critical value Z _?    is a point on the curve of the sampling distribution of the test statistic under the null hypothesis beyond which the null hypothesis is rejected at ? % level of significance.

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Suppose X~Normal(m,sigma²)

we have a random sample X_1,X₂,...,X_n of size n

where sigma is unknown

we are to test the null hypothesis

H ₀: m=m₁

Against the alternative hypothesis

H₁: m not equal to m₁

The test statistic is given by T=[ (xbar-m₁)]/[(s/sqrt(n))]

where xbar= sample mean

we estimate sigma by sample variance s

Which under H₀ follows t distribution with degrees of freedom (n-1)

We reject H₀ against H₁ at ? % level of significance if observed value of

|T | > t_?/2;(n-1)

where t_?/2;(n-1) is upper (?/2) point of t_(n-1)distribution.

here t_?/2;(n-1) is the critical value of the testing problem.

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