onChange of Pick list value Another Page block section should be Rendered

Hi,

 Create VF page , i.e onChange of pick list value Stage to 'closed lost' Another page block section should visible, if you select another stage value it should be hide.

See the code below,

  <apex:page standardController="Opportunity" sidebar="false">

    <apex:sectionHeader title="Edit Opportunity" subtitle="{!opportunity.name}"/>

    <apex:form >

        <apex:pageBlock title="Edit Opportunity" id="thePageBlock" mode="edit">

            <apex:pageMessages />

            <apex:pageBlockButtons >

                <apex:commandButton value="Save" action="{!save}"/>

                <apex:commandButton value="Cancel" action="{!cancel}"/>                

            </apex:pageBlockButtons>

            <apex:actionRegion >

                <apex:pageBlockSection title="Basic Information" columns="1">

                    <apex:inputField value="{!opportunity.name}"/>

                    <apex:pageBlockSectionItem >

                        <apex:outputLabel value="Stage"/>

                        <apex:outputPanel >

                            <apex:inputField value="{!opportunity.stageName}">

                                <apex:actionSupport event="onchange" rerender="thePageBlock"

                                                    status="status"/>

                            </apex:inputField>

                            <apex:actionStatus startText="applying value..." id="status"/>

                        </apex:outputPanel>

                    </apex:pageBlockSectionItem>

                    <apex:inputField value="{!opportunity.amount}"/>

                    

                </apex:pageBlockSection>

            </apex:actionRegion>

 <!-- This is another page block section , it visible when stage is 'closed lost' --> 

            <apex:pageBlockSection title="Closed Lost Information" columns="1"

                                   rendered="{!opportunity.stageName == 'Closed Lost'}">

                <apex:inputField value="{!opportunity.closedate}"/>

                <apex:inputField value="{!opportunity.amount}"/>

            </apex:pageBlockSection>

        </apex:pageBlock>

    </apex:form>

</apex:page>