Complete the following hypothesis test.= 4.93H:o2 + 4.93 (Claim)82 = 6.27, a= 0.01 andn=11%3DFinda. The Critical Values Xand X%3Db. The Test Statistic x =The Chi-Square Test StatistiDegrees of(n – 1)s²п-1c. ConclusionO fail to reject the null hypothesis and do not support the claimO reject the null hypothesis and support the claim

Answered: Complete the following hypothesis test.…

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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Question

100%

Complete the following hypothesis test.
= 4.93
H:o2 + 4.93 (Claim)
82 = 6.27, a
= 0.01 andn=11
%3D
Find
a. The Critical Values X
and X
%3D
b. The Test Statistic x =
The Chi-Square Test Statisti
Degrees of
(n – 1)s²
п-1
c. Conclusion
O fail to reject the null hypothesis and do not support the claim
O reject the null hypothesis and support the claim

Expert Solution

Step 1

Let $x_{i}; (i = 1, 2, . . ., n)$ be the random sample of size n from the normal population with mean $μ$ and variance $σ^{2}$ then, to test whether the population variance is equal to the specified variance ${σ_{o}}^{2}$ or not, the testing procedure is given by:

Null hypothesis: H_o: $σ^{2} {= σ_{o}}^{2}$

Alternative hypothesis: H_a: $σ^{2} {\neq σ_{o}}^{2}$

Test statistics: $χ^{2} = \frac{(n - 1) s^{2}}{{σ_{o}}^{2}}$

where

s² is sample variance.
n is sample size.
$χ^{2}$ follows chi-square distribution with (n-1) degree of freedom.

Then comparing calculated $χ^{2}$ value with the tabulated $χ^{2}$ value at given level of significance and degree of freedom, we will accept or reject the hypothesis.

if calculated $χ^{2}$ value is greater than the tabulated $χ^{2}$ value at given level of significance and degree of freedom, we can not accept the hypothesis.
if calculated $χ^{2}$ value is less than the tabulated $χ^{2}$ value at given level of significance and degree of freedom, we can not reject the hypothesis.