SharePoint SPFieldChoice change selected value Powershell

I have a dropdownlist with below items

Item1

Item2

Item3

Item4

When you run below script it will update dropdown list selected value as "Item4" for all sharepoint list items.

            foreach ($item in $items)

            {

           

             $field = [Microsoft.SharePoint.SPFieldChoice]$item.Fields["DOC GROUP"];

             # Write-Host "ID" $field.id

             write-host "Choice Field:" $item.url  $field.Choices[3]

             $item["DOC GROUP"] =  $field.Choices[3]

             $item.SystemUpdate()  

#foreach ($str in $field.Choices)

                #{

                 #  Write-Host  $str;

               # }

            }