Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0002 362512 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0924 1212712 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0924 1212712 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.2183 4111416 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.2196 4139096 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.2203 4156808 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.2204 4173816 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.2211 4181552 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.2211 4181552 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2673 4816888 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2696 4902120 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2701 4923048 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2808 5087000 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2809 5087256 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Hypothesis Testing for the Variance or Standard Deviation

The sampling distribution for the variance of a normaldistribution with varianceisgiven by

This means that if a random sample of sizeistaken from a normally distributed population with variancethenthe random variablehasthedistributionwithdegreesof freedom.

To perform a hypothesis test for the hypothesis

  1. Is the population normal?

  2. State the null hypothesis– that-and the alternative hypothesis–that fora two tailed test OR that eitherORfora one tailed test.

  3. Find the test statistic Comparethis with the values of-two tailed test – or-ifisifis-from thetables.

  4. Rejectifthe test statistic falls into any of the shaded regions in thediagram below, else do not reject

Example: Conduct a hypothesis test at the 95% level to testwhether the variance of the population from which this sample istaken

3,4,3,4,5,6,2,3,4,5

is equal to 1.

Null Hypothesis,

Alternative Hypothesis,

The test statistic is

and

We do not reject

Add comment

Security code
Refresh