Command button not getting display on Vf page

I have create a command button on vf page. But Command button not getting display on Vf page.

My code

<apex:page controller="testpopup">
    <apex:form>
        <apex:pageBlock>
            <apex:pageBlockButtons>
                <apex:commandButton value="test" action="{!showpopup}" rendered="testpopup"></apex:commandButton>
            </apex:pageBlockButtons>
            <apex:pageBlockSection></apex:pageBlockSection>
        </apex:pageBlock>
        <apex:pageBlock>
        </apex:pageBlock>

        <apex:outputPanel id="testpopup">
            <apex:outputPanel styleClass="popupbackgroud" layout="block" rendered="{!displayPopUp}" />
            <apex:outputPanel styleClass="custPopup" layout="block" rendered="{!displayPopUp}">
                This is where I would put whatever information I needed to show to my end user.
                <br/>
                <br/>
                <br/>
                <apex:commandButton value="Hide Pop up" action="{!closePopup}" rerender="testpopup" />
            </apex:outputPanel>
        </apex:outputPanel>

    </apex:form>

    <style type="text/css">
        .custPopup {
            background-color: white;
            border-width: 2px;
            border-style: solid;
            z-index: 9999;
            left: 50%;
            padding: 10px;
            position: absolute;
            /* These are the 3 css properties you will need to change so the popup
            displays in the center of the screen. First set the width. Then set
            margin-left to negative half of what the width is. You can add
            the height property for a fixed size pop up if you want.*/
            width: 500px;
            margin-left: -250px;
            top: 100px;
        }
        .popupBackground {
            background-color: black;
            opacity: 0.20;
            filter: alpha(opacity=20);
            position: absolute;
            width: 100%;
            height: 100%;
            top: 0;
            left: 0;
            z-index: 9998;
        }
    </style>


</apex:page>

i am new in salesforce. Please let me know what is getting wrong .